{"results":[{"id":"arxiv_2001.05128","title":"Extension of frames and bases -- II","authors":[{"name":"Mahesh Krishna K."},{"name":"P. Sam Johnson"}],"abstract":"Operator-valued frame ($G$-frame), as a generalization of frame is introduced by Kaftal, Larson, and Zhang in \\textit{Trans. Amer. Math. Soc.}, 361(12):6349-6385, 2009 and by Sun in \\textit{J. Math. Anal. Appl.}, 322(1):437-452, 2006. It has been further extended in the paper arXiv:1810.01629 [math.OA] 3 October 2018, so as to have a rich theory on operator-valued frames for Hilbert spaces as well as for Banach spaces. The continuous version has been studied in this paper when the indexing set is a measure space. We study duality, similarity, orthogonality and stability of this extension. Several characterizations are given including a notable characterization when the measure space is a locally compact group. Variation formula, dimension formula and trace formula are derived when the Hilbert space is finite dimensional.","source":"arXiv","year":2020,"language":"en","subjects":["math.FA","math.OA"],"url":"https://arxiv.org/abs/2001.05128","pdf_url":"https://arxiv.org/pdf/2001.05128","is_open_access":true,"published_at":"2020-01-15T04:22:37Z","score":64},{"id":"ss_dd427bb8dafd72590522ed1b02c1fa6364612de6","title":"CCR and CAR flows over convex cones","authors":[{"name":"R. Srinivasan"}],"abstract":"Recently it is proved in arXiv:1906.05493v1 [math.OA] that CCR flows over convex cones are cocycle conjugate if and only if the associated isometric representations are conjugate. We provide a very short, simple and direct proof of that. Using the same idea we prove the analogous statement for CAR flows as well. Further we show that CCR flows are not cocycle conjugate to the CAR flows when the (multi-parameter) isometric representation is `proper', a condition which is satisfied by all known examples.","source":"Semantic Scholar","year":2019,"language":"en","subjects":["Mathematics"],"url":"https://www.semanticscholar.org/paper/dd427bb8dafd72590522ed1b02c1fa6364612de6","is_open_access":true,"citations":4,"published_at":"","score":63.12},{"id":"ss_2deafead8fb909c7fbafcfdfb46b07525baa93b2","title":"Mathematics, Signal Processing and Linear Systems New Problems and Directions","authors":[{"name":"D. Alpay"},{"name":"J. Ball"},{"name":"G. Groenewald"}],"abstract":"","source":"Semantic Scholar","year":2017,"language":"en","subjects":null,"url":"https://www.semanticscholar.org/paper/2deafead8fb909c7fbafcfdfb46b07525baa93b2","is_open_access":true,"citations":2,"published_at":"","score":61.06},{"id":"ss_248d1e181a478b97ec509202d05002b42b220a21","title":"An alternative characterization of normed interpolation spaces between $\\ell^{1}$ and $\\ell^{q}$","authors":[{"name":"M. Cwikel"},{"name":"Per G. Nilsson"}],"abstract":"Given a constant $q\\in(1,\\infty)$, we study the following property of a normed sequence space $E$: ===================== If $\\left\\{ x_{n}\\right\\}_{n\\in\\mathbb{N}}$ is an element of $E$ and if $\\left\\{ y_{n}\\right\\}_{n\\in\\mathbb{N}}$ is an element of $\\ell^{q}$ such that $\\sum_{n=1}^{\\infty}\\left|x_{n}\\right|^{q}=\\sum_{n=1}^\\infty \\left|y_{n}\\right|^{q}$ and if the nonincreasing rearrangements of these two sequences satisfy $\\sum_{n=1}^{N}\\left|x_{n}^{*}\\right|^{q}\\le\\sum_{n=1}^{N}\\left|y_{n}^{*}\\right|^{q}$ for all $N\\in\\mathbb{N}$, then $\\left\\{ y_{n}\\right\\}_{n\\in\\mathbb{N}}\\in E$ and $\\left\\Vert \\left\\{ y_{n}\\right\\}_{n\\in\\mathbb{N}}\\right\\Vert_{E}\\le C\\left\\Vert \\left\\{ x_{n}\\right\\}_{n\\in\\mathbb{N}}\\right\\Vert_{E}$ for some constant $C$ which depends only on $E$. ===================== We show that this property is very close to characterizing the normed interpolation spaces between $\\ell^{1}$ and $\\ell^{q}$. More specificially, we first show that every space which is a normed interpolation space with respect to the couple $\\left(\\ell^{p},\\ell^{q}\\right)$ for some $p\\in[1,q]$ has the above mentioned property. Then we show, conversely, that if $E$ has the above mentioned property, and also has the Fatou property, and is contained in $\\ell^{q}$, then it is a normed interpolation space with respect to the couple $\\left(\\ell^{1},\\ell^{q}\\right)$. These results are our response to a conjecture of Galina Levitina, Fedor Sukochev and Dmitriy Zanin in arXiv:1703.04254v1 [math.OA].","source":"Semantic Scholar","year":2017,"language":"en","subjects":["Mathematics"],"url":"https://www.semanticscholar.org/paper/248d1e181a478b97ec509202d05002b42b220a21","is_open_access":true,"citations":1,"published_at":"","score":61.03},{"id":"ss_e346b109c937ee49bae8a05f78bdd78a8b122315","title":"The index of product systems of Hilbert modules: Two equivalent definitions","authors":[{"name":"B. Vujošević"}],"abstract":"","source":"Semantic Scholar","year":2015,"language":"en","subjects":["Mathematics"],"doi":"10.2298/PIM141114001V","url":"https://www.semanticscholar.org/paper/e346b109c937ee49bae8a05f78bdd78a8b122315","pdf_url":"http://www.doiserbia.nb.rs/ft.aspx?id=0350-13021511049V","is_open_access":true,"citations":3,"published_at":"","score":59.09},{"id":"ss_eaa3547253893bee1b20c0261c695dd8a96d05fb","title":"Constructing the extended Haagerup planar algebra","authors":[{"name":"S. Bigelow"},{"name":"E. Peters"},{"name":"S. Morrison"},{"name":"Noah Snyder"}],"abstract":"We construct a new subfactor planar algebra, and as a corollary a new subfactor, with the ‘extended Haagerup’ principal graph pair. This completes the classification of irreducible amenable subfactors with index in the range ($$ {4},{3} + \\sqrt {{3}} $$), which was initiated by Haagerup in 1993. We prove that the subfactor planar algebra with these principal graphs is unique. We give a skein-theoretic description, and a description as a subalgebra generated by a certain element in the graph planar algebra of its principal graph. In the skein-theoretic description there is an explicit algorithm for evaluating closed diagrams. This evaluation algorithm is unusual because intermediate steps may increase the number of generators in a diagram. This is the published version of arXiv:0909.4099 [math.OA].","source":"Semantic Scholar","year":2009,"language":"en","subjects":["Mathematics"],"doi":"10.1007/s11511-012-0081-7","url":"https://www.semanticscholar.org/paper/eaa3547253893bee1b20c0261c695dd8a96d05fb","pdf_url":"https://projecteuclid.org/journals/acta-mathematica/volume-209/issue-1/Constructing-the-extended-Haagerup-planar-algebra/10.1007/s11511-012-0081-7.pdf","is_open_access":true,"citations":110,"published_at":"","score":56.3},{"id":"arxiv_1001.3890","title":"A Simple Separable Exact C*-Algebra not Anti-isomorphic to Itself","authors":[{"name":"N. Christopher Phillips"},{"name":"Maria Grazia Viola"}],"abstract":"We give an example of an exact, stably finite, simple. separable C*-algebra D which is not isomorphic to its opposite algebra. Moreover, D has the following additional properties. It is stably finite, approximately divisible, has real rank zero and stable rank one, has a unique tracial state, and the order on projections over D is determined by traces. It also absorbs the Jiang-Su algebra Z, and in fact absorbs the 3^{\\infty} UHF algebra. We can also explicitly compute the K-theory of D, namely K_0 (D) = Z[1/3] with the standard order, and K_1 (D) = 0, as well as the Cuntz semigroup of D.","source":"arXiv","year":2010,"language":"en","subjects":["math.OA"],"doi":"10.1007/s00208-011-0755-z","url":"https://arxiv.org/abs/1001.3890","pdf_url":"https://arxiv.org/pdf/1001.3890","is_open_access":true,"published_at":"2010-01-21T22:11:35Z","score":54},{"id":"crossref_10.63485/761av-mah66","title":"New OA math journal","authors":[{"name":"Gavin Baker"}],"abstract":"The Bulletin of Mathematical Analysis and Applications is a new OA journal. The inaugural issue is now available.","source":"CrossRef","year":2009,"language":"en","subjects":null,"doi":"10.63485/761av-mah66","url":"https://doi.org/10.63485/761av-mah66","pdf_url":"https://api.rogue-scholar.org/posts/10.63485/761av-mah66.pdf","is_open_access":true,"published_at":"","score":53},{"id":"ss_e6380e4e80897ec9dcacb333bb511706a1ed6961","title":"Quasidiagonal C ∗ -algebras and Nonstandard Analysis”-Arxiv preprint math.OA/0209292, 2002 - arxiv.org","authors":[{"name":"J. Thayer"},{"name":"J. Thayer"}],"abstract":"","source":"Semantic Scholar","year":2008,"language":"en","subjects":null,"url":"https://www.semanticscholar.org/paper/e6380e4e80897ec9dcacb333bb511706a1ed6961","is_open_access":true,"citations":1,"published_at":"","score":52.03},{"id":"crossref_10.63485/2dhgv-px397","title":"OA math, physics, and chemistry for Africa","authors":[{"name":"Peter Suber"}],"abstract":"The same group that launched e-Math for Africa in 2006 is now working on e-Physics for Africa and e-Chemistry for Africa.  (Thanks to Anders Wändahl.) The goal of e-Math for Africa is \u0026#34;to coordinate the efforts to make an African consortium for e-journals and databases.\u0026#34;  It includes both OA journals and TA journals discounted for African researchers.","source":"CrossRef","year":2008,"language":"en","subjects":null,"doi":"10.63485/2dhgv-px397","url":"https://doi.org/10.63485/2dhgv-px397","pdf_url":"https://api.rogue-scholar.org/posts/10.63485/2dhgv-px397.pdf","is_open_access":true,"published_at":"","score":52},{"id":"crossref_10.63485/e8y8p-f0793","title":"New OA journal of computer science and math","authors":[{"name":"Gavin Baker"}],"abstract":"The International Journal of Open Problems in Computer Science and Mathematics is a new, peer-reviewed, no-fee OA journal. The inaugural issue, dated June 2008, is now online.","source":"CrossRef","year":2008,"language":"en","subjects":null,"doi":"10.63485/e8y8p-f0793","url":"https://doi.org/10.63485/e8y8p-f0793","pdf_url":"https://api.rogue-scholar.org/posts/10.63485/e8y8p-f0793.pdf","is_open_access":true,"published_at":"","score":52},{"id":"crossref_10.63485/ypae3-7py06","title":"Math societies critique impact factor, mention OA advantage","authors":[{"name":"Gavin Baker"}],"abstract":"Robert Adler, et al., Citation Statistics, a report by the International Mathematical Union, the International Council of Industrial and Applied Mathematics, and the Institute of Mathematical Statistics, June 12, 2008.","source":"CrossRef","year":2008,"language":"en","subjects":null,"doi":"10.63485/ypae3-7py06","url":"https://doi.org/10.63485/ypae3-7py06","pdf_url":"https://api.rogue-scholar.org/posts/10.63485/ypae3-7py06.pdf","is_open_access":true,"published_at":"","score":52},{"id":"crossref_10.63485/nd9vn-wa433","title":"Plans for an OA repository of video modules in math and science","authors":[{"name":"Peter Suber"}],"abstract":"MIT helps launch interactive video education project in Jordan, a press release from MIT, November 13, 2008.","source":"CrossRef","year":2008,"language":"en","subjects":null,"doi":"10.63485/nd9vn-wa433","url":"https://doi.org/10.63485/nd9vn-wa433","pdf_url":"https://api.rogue-scholar.org/posts/10.63485/nd9vn-wa433.pdf","is_open_access":true,"published_at":"","score":52},{"id":"ss_6f7947f26e185870bc7a3f92594577149fd6ea6c","title":"The antipode: a fascinating concept","authors":[{"name":"A. V. Daele"}],"abstract":"","source":"Semantic Scholar","year":2008,"language":"en","subjects":["Mathematics"],"url":"https://www.semanticscholar.org/paper/6f7947f26e185870bc7a3f92594577149fd6ea6c","is_open_access":true,"published_at":"","score":52},{"id":"ss_c905f92e7e445bf3f3b4ac4c4256f900e81a6e7b","title":"Every compact group arises as the outer automorphism group of a II_1 factor","authors":[{"name":"S'ebastien Falguieres"},{"name":"S. Vaes"}],"abstract":"We show that any compact group can be realized as the outer automorphism group of a factor of type II1. This has been proved in the abelian case by Ioana, Peterson and Popa [A. Ioana, J. Peterson, S. Popa, Amalgamated free products of w-rigid factors and calculation of their symmetry group, math.OA/0505589, Acta Math., in press] applying Popa's deformation/rigidity techniques to amalgamated free product von Neumann algebras. Our methods are a generalization of theirs.","source":"Semantic Scholar","year":2007,"language":"en","subjects":["Mathematics"],"doi":"10.1016/J.JFA.2008.02.002","url":"https://www.semanticscholar.org/paper/c905f92e7e445bf3f3b4ac4c4256f900e81a6e7b","pdf_url":"https://lirias.kuleuven.be/bitstream/123456789/177028/2/out-compact.pdf","is_open_access":true,"citations":20,"published_at":"","score":51.6},{"id":"ss_46d5343aa35f0f0b90b036e1df71da61034e09e1","title":"Dimensions and spectral triples for fractals in R^N","authors":[{"name":"D. Guido"},{"name":"T. Isola"}],"abstract":"Two spectral triples are introduced for a class of fractals in R^n. The definitions of noncommutative Hausdorff dimension and noncommutative tangential dimensions, as well as the corresponding Hausdorff and Hausdorff-Besicovitch functionals considered in math.OA/0202108, are studied for the mentioned fractals endowed with these spectral triples, showing in many cases their correspondence with classical objects. In particular, for any limit fractal, the Hausdorff-Besicovitch functionals do not depend on the generalized limit procedure.","source":"Semantic Scholar","year":2004,"language":"en","subjects":["Mathematics"],"url":"https://www.semanticscholar.org/paper/46d5343aa35f0f0b90b036e1df71da61034e09e1","is_open_access":true,"citations":43,"published_at":"","score":51.29},{"id":"crossref_10.63485/39n9p-z4s21","title":"OA math, not meth","authors":[{"name":"Peter Suber"}],"abstract":"Martin Smith is the coordinator of a Canadian methamphetamine treatment community called Camp One.  Its motto is \u003cem\u003e Math Not Meth. \u003c/em\u003e He wrote to me recently to explain that Here's a little more background from the Math Not Meth blog: And a little more from one of Smith's emails: Finally, some detail from a recent Smith comment on another blog: \u003cstrong\u003e Comment \u003c/strong\u003e .  This is a remarkable story.","source":"CrossRef","year":2007,"language":"en","subjects":null,"doi":"10.63485/39n9p-z4s21","url":"https://doi.org/10.63485/39n9p-z4s21","pdf_url":"https://api.rogue-scholar.org/posts/10.63485/39n9p-z4s21.pdf","is_open_access":true,"published_at":"","score":51},{"id":"crossref_10.63485/w24vp-0rf74","title":"OA math textbooks opening wider","authors":[{"name":"Peter Suber"}],"abstract":"David Santos is making Openmathtext.org even more open by permitting rather than blocking commercial use.","source":"CrossRef","year":2007,"language":"en","subjects":null,"doi":"10.63485/w24vp-0rf74","url":"https://doi.org/10.63485/w24vp-0rf74","pdf_url":"https://api.rogue-scholar.org/posts/10.63485/w24vp-0rf74.pdf","is_open_access":true,"published_at":"","score":51},{"id":"ss_b7d88a9c6d8fbc03e530dc86fb1a2e8d66e1ea80","title":"Strict weak mixing of some C∗-dynamical systems based on free shifts","authors":[{"name":"F. Fidaleo"},{"name":"F. Mukhamedov"}],"abstract":"Abstract We define a stronger property than unique ergodicity with respect to the fixed-point subalgebra firstly investigated in [B. Abadie, K. Dykema, Unique ergodicity of free shifts and some other automorphisms of C ∗ -algebras, math.OA/0608227 ]. Such a property is denoted as F-strict weak mixing (F stands for the unital completely positive projection onto the fixed-point operator system). Then we show that the free shifts on the reduced C ∗ -algebras of RD-groups, including the free group on infinitely many generators, and amalgamated free product C ∗ -algebras, considered in [B. Abadie, K. Dykema, Unique ergodicity of free shifts and some other automorphisms of C ∗ -algebras, math.OA/0608227 ], are all strictly weak mixing and not only uniquely ergodic.","source":"Semantic Scholar","year":2006,"language":"en","subjects":["Mathematics"],"doi":"10.1016/j.jmaa.2007.02.066","url":"https://www.semanticscholar.org/paper/b7d88a9c6d8fbc03e530dc86fb1a2e8d66e1ea80","pdf_url":"https://doi.org/10.1016/j.jmaa.2007.02.066","is_open_access":true,"citations":23,"published_at":"","score":50.69}],"total":1083300,"page":1,"page_size":20,"sources":["CrossRef","arXiv","Semantic Scholar"],"query":"math.OA"}