{"results":[{"id":"ss_f473c172f5cb9bec0d77584041e3a521b4fd63b2","title":"Comments on Symplectic bipotentials arXiv:2410.23122","authors":[{"name":"Marius Buliga"}],"abstract":"This is a reaction to the article Symplectic bipotentials, in published form [2] and in preprint form [1] arXiv:2410.23122v1. We give evidence that most of the content of the article [2] is already covered in previous works, partially cited like [7] arXiv:0810.1419 [math.FA], or uncited, like [10] arXiv:1902.04598 [math-ph], [3] arXiv:2304.14158 [math-ph], which already introduced and studied symplectic bipotentials.","source":"Semantic Scholar","year":2026,"language":"en","subjects":["Mathematics"],"url":"https://www.semanticscholar.org/paper/f473c172f5cb9bec0d77584041e3a521b4fd63b2","is_open_access":true,"published_at":"","score":70},{"id":"ss_d4008bf012803e90c50bf4f113d41fee3c4c8004","title":"A small Radon-Nikod\\'ym compact space from a parametrized diamond","authors":[{"name":"Arturo Mart'inez-Celis"},{"name":"Adam Morawski"}],"abstract":"A compact space $K$ is Radon-Nikod\\'{y}m if there is a lower semi-continuous metric fragmenting $K$. In this note, we show that, under $\\diamondsuit (\\mathrm{non}{\\mathcal{M}})$, there is a Radon-Nikod\\'{y}m compact space of weight $\\aleph_1$ with a continuous image that is not Radon-Nikod\\'{y}m, which partially answers a question posed in arXiv:1112.4152 [math.FA].","source":"Semantic Scholar","year":2025,"language":"en","subjects":["Mathematics"],"url":"https://www.semanticscholar.org/paper/d4008bf012803e90c50bf4f113d41fee3c4c8004","is_open_access":true,"published_at":"","score":69},{"id":"ss_21c78d210f6c3b68e6b9bc2a2bd03a97c3b36cbb","title":"Lipschitz Homotopy Groups of Contact 3-Manifolds","authors":[{"name":"Daniel Perry"}],"abstract":"We study contact 3-manifolds using the techniques of sub-Riemannian geometry and geometric measure theory, in particular establishing properties of their Lipschitz homotopy groups. We prove a biLipschitz version of the Theorem of Darboux: a contact $(2n+1)$-manifold endowed with a sub-Riemannian structure is locally biLipschitz equivalent to the Heisenberg group $\\mathbb{H}^n$ with its Carnot-Caratheodory metric. Then each contact $(2n+1)$-manifold endowed with a sub-Riemannian structure is purely $k$-unrectifiable for $k\u003en$. We extend results of Dejarnette et al. (arXiv:1109.4641 [math.FA]) and Wenger and Young (arXiv:1210.6943 [math.GT]) by showing for any purely 2-unrectifiable sub-Riemannian manifold $(M,\\xi,g)$ that the $n$th Lipschitz homotopy group is trivial for $n\\geq2$ and that the set of oriented, horizontal knots in $(M,\\xi)$ injects into the first Lipschitz homotopy group. Thus, the first Lipschitz homotopy group of any contact 3-manifold is uncountably generated. Therefore, in the sense of Lipschitz homotopy groups, a contact 3-manifold is a $K(\\pi,1)$-space for an uncountably generated group $\\pi$. Finally, we prove that each open distributional embedding between purely 2-unrectifiable sub-Riemannian manifolds induces an injective map on the associated first Lipschitz homotopy groups. Therefore, each open subset of a contact 3-manifold determines an uncountable subgroup of the first Lipschitz homotopy group of the contact 3-manifold.","source":"Semantic Scholar","year":2020,"language":"en","subjects":["Mathematics"],"doi":"10.14321/realanalexch.47.1.1598582300","url":"https://www.semanticscholar.org/paper/21c78d210f6c3b68e6b9bc2a2bd03a97c3b36cbb","pdf_url":"https://arxiv.org/pdf/2008.06928","is_open_access":true,"citations":4,"published_at":"","score":64.12},{"id":"crossref_10.1007/s11464-020-0832-2","title":"On spectrum of Hermitizable tridiagonal matrices","authors":[{"name":"Mu-Fa Chen"}],"abstract":"","source":"CrossRef","year":2020,"language":"en","subjects":null,"doi":"10.1007/s11464-020-0832-2","url":"https://doi.org/10.1007/s11464-020-0832-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11464-020-0832-2.pdf","is_open_access":true,"citations":3,"published_at":"","score":64.09},{"id":"ss_0c912f4ab1b723cbbc6f31ae2bb34b7a11ec066d","title":"Topological lattice rings with $AM$-property","authors":[{"name":"O. Zabeti"}],"abstract":"Motivated by the recent definition of $AM$-property in locally solid vector lattices [O. Zabeti, arXiv: 1912.00141v2 [math.FA]], in this note, we try to investigate those results in the category of all locally solid lattice rings. In fact, we characterize locally solid lattice rings in which order bounded sets and bounded sets agree. Furthermore, with the aid of $AM$-property, we find conditions under that, order bounded group homomorphisms and different types of bounded group homomorphisms coincide. Moreover, we show that each class of bounded order bounded group homomorphisms on a locally solid lattice ring $X$ has the Lebegsue or the Levi property if and only if so is $X$.","source":"Semantic Scholar","year":2020,"language":"en","subjects":["Mathematics"],"url":"https://www.semanticscholar.org/paper/0c912f4ab1b723cbbc6f31ae2bb34b7a11ec066d","is_open_access":true,"published_at":"","score":64},{"id":"ss_6d3efacbdfab40c677d8920f1c4a56a7429a19e3","title":"Embeddability of ℓ and bases in Lipschitz free p-spaces for 0 \u003c p ≤ 1","authors":[{"name":"F. Albiac"},{"name":"J. L. Ansorena"},{"name":"Marek Cúth"},{"name":"M. Doucha"}],"abstract":"Our goal in this paper is to continue the study initiated by the authors in [Lipschitz free $p$-spaces for $0\u003cp\u003c1$; arXiv:1811.01265 [math.FA]] of the geometry of the Lipschitz free $p$-spaces over quasimetric spaces for $0\u003cp\\le1$, denoted $\\mathcal F_{p}(\\mathcal M)$. Here we develop new techniques to show that, by analogy with the case $p=1$, the space $\\ell_{p}$ embeds isomorphically in $\\mathcal F_{p}(\\mathcal M)$ for $0\u003cp\u003c1$. Going further we see that despite the fact that, unlike the case $p=1$, this embedding need not be complemented in general, complementability of $\\ell_{p}$ in a Lipschitz free $p$-space can still be attained by imposing certain natural restrictions to $\\mathcal M$. As a by-product of our discussion on basis in $\\mathcal F_{p}([0,1])$, we obtain the first-known examples of $p$-Banach spaces for $p\u003c1$ that possess a basis but fail to have an unconditional basis.","source":"Semantic Scholar","year":2019,"language":"en","subjects":["Mathematics"],"doi":"10.1016/J.JFA.2019.108354","url":"https://www.semanticscholar.org/paper/6d3efacbdfab40c677d8920f1c4a56a7429a19e3","pdf_url":"https://doi.org/10.1016/j.jfa.2019.108354","is_open_access":true,"citations":8,"published_at":"","score":63.24},{"id":"crossref_10.1007/s11464-019-0799-z","title":"Improved global algorithms for maximal eigenpair","authors":[{"name":"Mu-Fa Chen"},{"name":"Yue-Shuang Li"}],"abstract":"","source":"CrossRef","year":2019,"language":"en","subjects":null,"doi":"10.1007/s11464-019-0799-z","url":"https://doi.org/10.1007/s11464-019-0799-z","pdf_url":"http://link.springer.com/content/pdf/10.1007/s11464-019-0799-z.pdf","is_open_access":true,"published_at":"","score":63},{"id":"crossref_10.1007/s11464-018-0716-x","title":"Hermitizable, isospectral complex matrices or differential operators","authors":[{"name":"Mu-Fa Chen"}],"abstract":"","source":"CrossRef","year":2018,"language":"en","subjects":null,"doi":"10.1007/s11464-018-0716-x","url":"https://doi.org/10.1007/s11464-018-0716-x","pdf_url":"http://link.springer.com/content/pdf/10.1007/s11464-018-0716-x.pdf","is_open_access":true,"citations":7,"published_at":"","score":62.21},{"id":"ss_34992dc20d8471328e4f1bd6ab9e56611c9dc34c","title":"Spectra of anticommutator for two orthogonal projections","authors":[{"name":"Yan-Ni Dou"},{"name":"Yue-qing Wang"},{"name":"Miaomiao Cui"},{"name":"H. Du"}],"abstract":"ABSTRACT In this note, for any two orthogonal projections P,Q on a Hilbert space, the characterization of spectrum of anticommutator PQ+QP has been obtained. As a corollary, an alternative proof of the norm formula has been obtained (see Walters S. Anticommutator norm formula for projection operators, arXiv:1604.00699vl [math.FA] 3 Apr 2016).","source":"Semantic Scholar","year":2018,"language":"en","subjects":["Mathematics"],"doi":"10.1080/03081087.2018.1481358","url":"https://www.semanticscholar.org/paper/34992dc20d8471328e4f1bd6ab9e56611c9dc34c","pdf_url":"https://arxiv.org/pdf/1705.05866","is_open_access":true,"citations":3,"published_at":"","score":62.09},{"id":"crossref_10.1007/s11464-017-0658-8","title":"Global algorithms for maximal eigenpair","authors":[{"name":"Mu-Fa Chen"}],"abstract":"","source":"CrossRef","year":2017,"language":"en","subjects":null,"doi":"10.1007/s11464-017-0658-8","url":"https://doi.org/10.1007/s11464-017-0658-8","pdf_url":"http://link.springer.com/content/pdf/10.1007/s11464-017-0658-8.pdf","is_open_access":true,"citations":6,"published_at":"","score":61.18},{"id":"ss_105551cd77f91c505310f3ea5e93efcd463a000d","title":"Optimality of the rearrangement inequality with applications to Lorentz-type sequence spaces","authors":[{"name":"F. Albiac"},{"name":"J. L. Ansorena"},{"name":"D. Leung"},{"name":"B. Wallis"}],"abstract":"We characterize the sequences $(w_i)_{i=1}^\\infty$ of non-negative numbers for which \\[ \\sum_{i=1}^\\infty a_i w_i \\quad \\text{ is of the same order as } \\quad \\sup_n \\sum_{i=1}^n a_i w_{1+n-i} \\] when $(a_i)_{i=1}^\\infty$ runs over all non-increasing sequences of non-negative numbers. As a by-product of our work we settle a problem raised in [F. Albiac, Jose L. Ansorena and B. Wallis; arXiv:1703.07772[math.FA]] and prove that Garling sequences spaces have no symmetric basis.","source":"Semantic Scholar","year":2017,"language":"en","subjects":["Mathematics"],"doi":"10.7153/MIA-2018-21-10","url":"https://www.semanticscholar.org/paper/105551cd77f91c505310f3ea5e93efcd463a000d","pdf_url":"http://files.ele-math.com/abstracts/mia-21-10-abs.pdf","is_open_access":true,"citations":4,"published_at":"","score":61.12},{"id":"ss_53a13204f2603f7b598408203dc5375b562d6fab","title":"Spectra of anticommutator for two orthogonal projections","authors":[{"name":"Yan-Ni Dou"},{"name":"H. Du"},{"name":"Yue-qing Wang"}],"abstract":"In this note, for any two orthogonal projection $P,Q$ on a Hilbert space, the characterization of spectrum of anticommutator $PQ+QP$ has been obtained. As a corollary, the norm formula $$\\parallel PQ+QP\\parallel=\\parallel PQ\\parallel+\\parallel PQ\\parallel^2$$ has been got an alternative proof (see Sam Waltrs, Anticommutator norm formula for projection operators, arXiv:1604.00699vl [math.FA] 3 Apr 2016)","source":"Semantic Scholar","year":2017,"language":"en","subjects":["Mathematics"],"url":"https://www.semanticscholar.org/paper/53a13204f2603f7b598408203dc5375b562d6fab","is_open_access":true,"citations":3,"published_at":"","score":61.09},{"id":"ss_2546c6e68ba2601adc8c37518ee26a507c61ad84","title":"Fixed point approximation of Picard normal S-iteration process for generalized nonexpansive mappings in hyperbolic spaces","authors":[{"name":"M. Imdad"},{"name":"S. Dashputre"}],"abstract":"In this paper, we establish strong and $$\\Delta$$Δ-convergence theorems for a relatively new iteration process generated by generalized nonexpansive mappings in uniformly convex hyperbolic spaces. The theorems presented in this paper generalizes corresponding theorems for uniformly convex normed spaces of Kadioglu and Yildirim (Approximating fixed points of nonexpansive mappings by faster iteration process, arXiv:1402.6530v1 [math.FA], 2014) and CAT(0)-spaces of Abbas et al. (J Inequal Appl 2014:212, 2014) and many others in this direction.","source":"Semantic Scholar","year":2016,"language":"en","subjects":["Mathematics"],"doi":"10.1007/S40096-016-0187-8","url":"https://www.semanticscholar.org/paper/2546c6e68ba2601adc8c37518ee26a507c61ad84","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs40096-016-0187-8.pdf","is_open_access":true,"citations":20,"published_at":"","score":60.6},{"id":"crossref_10.1007/s11464-016-0573-4","title":"Efficient initials for computing maximal eigenpair","authors":[{"name":"Mu-Fa Chen"}],"abstract":"","source":"CrossRef","year":2016,"language":"en","subjects":null,"doi":"10.1007/s11464-016-0573-4","url":"https://doi.org/10.1007/s11464-016-0573-4","pdf_url":"http://link.springer.com/content/pdf/10.1007/s11464-016-0573-4.pdf","is_open_access":true,"citations":7,"published_at":"","score":60.21},{"id":"ss_882a8a50842a8f3a3326008134404a6c2d48dfec","title":"Additive Units of Product System of Hilbert Modules","authors":[{"name":"B. Vujošević"}],"abstract":"","source":"Semantic Scholar","year":2016,"language":"en","subjects":["Mathematics"],"url":"https://www.semanticscholar.org/paper/882a8a50842a8f3a3326008134404a6c2d48dfec","is_open_access":true,"citations":3,"published_at":"","score":60.09},{"id":"ss_1f5a7dc0732330af09a1696e40770afcc5f6fcdc","title":"Holomorphic functions on the quantum polydisk and on the quantum ball","authors":[{"name":"A. Pirkovskii"}],"abstract":"We introduce and study noncommutative (or ``quantized'') versions of the algebras of holomorphic functions on the polydisk and on the ball in $\\mathbb C^n$. Specifically, for each $q\\in\\mathbb C\\setminus\\{ 0\\}$ we construct Fr\\'echet algebras $\\mathcal O_q(\\mathbb D^n)$ and $\\mathcal O_q(\\mathbb B^n)$ such that for $q=1$ they are isomorphic to the algebras of holomorphic functions on the open polydisk $\\mathbb D^n$ and on the open ball $\\mathbb B^n$, respectively. In the case where $0\u003cq\u003c1$, we establish a relation between our holomorphic quantum ball algebra $\\mathcal O_q(\\mathbb B^n)$ and L. L. Vaksman's algebra $C_q(\\bar{\\mathbb B}^n)$ of continuous functions on the closed quantum ball. Finally, we show that $\\mathcal O_q(\\mathbb D^n)$ and $\\mathcal O_q(\\mathbb B^n)$ are not isomorphic provided that $|q|=1$ and $n\\ge 2$. This result can be interpreted as a $q$-analog of Poincar\\'e's theorem, which asserts that $\\mathbb D^n$ and $\\mathbb B^n$ are not biholomorphically equivalent unless $n=1$. This paper replaces the first part of Version 1: arXiv:1508.05768v1 [math.FA].","source":"Semantic Scholar","year":2015,"language":"en","subjects":["Mathematics"],"doi":"10.4171/JNCG/340","url":"https://www.semanticscholar.org/paper/1f5a7dc0732330af09a1696e40770afcc5f6fcdc","is_open_access":true,"citations":7,"published_at":"","score":59.21},{"id":"crossref_10.1007/s40304-014-0028-8","title":"Isospectral Operators","authors":[{"name":"Mu-Fa Chen"},{"name":"Xu Zhang"}],"abstract":"","source":"CrossRef","year":2014,"language":"en","subjects":null,"doi":"10.1007/s40304-014-0028-8","url":"https://doi.org/10.1007/s40304-014-0028-8","pdf_url":"http://link.springer.com/content/pdf/10.1007/s40304-014-0028-8.pdf","is_open_access":true,"citations":8,"published_at":"","score":58.24}],"total":1116876,"page":1,"page_size":20,"sources":["DOAJ","CrossRef","Semantic Scholar"],"query":"math.FA"}