arXiv Open Access 2019

Theory of $B(X)$-module -Algebraic module structure of generally-unbounded infinitesimal generators-

Yoritaka Iwata

Lihat Sumber

Abstrak

The concept of logarithmic representation of infinitesimal generators is introduced, and it is applied to clarify the algebraic structure of bounded and unbounded infinitesimal generators. In particular, by means of the logarithmic representation, the bounded components can be extracted from generally-unbounded infinitesimal generators. In conclusion the concept of module over a Banach algebra is proposed as the generalization of Banach algebra. As an application to mathematical physics, the rigorous formulation of rotation group, which consists of unbounded operators being written by differential operators, is provided using the module over a Banach algebra.

Topik & Kata Kunci

math.FA math-ph math.OA

Penulis (1)

Yoritaka Iwata

Format Sitasi

APA MLA BibTeX

Iwata, Y. (2019). Theory of $B(X)$-module -Algebraic module structure of generally-unbounded infinitesimal generators-. https://arxiv.org/abs/1907.08767

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2019
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓