A seminorm with square property on a Banach algebra is submultiplicative-Reference-Cited by-同舟云学术

A seminorm with square property on a Banach algebra is submultiplicative

Published:1993 Issue:2 Volume:117 Page:435-438
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Bhatt S. J.

Abstract

The result stated in the title is proved in a Banach algebra and is used to discuss (i) commutativity criteria in normed algebras, (ii) uniqueness of the uniform norm in uniform Banach algebras, and (iii) existence of continuous multiplicative linear functionals on topological algebras together with a simple reduction of the Michael problem in Fréchet algebras. Submultiplicativity does not imply subadditivity in the presence of the square property.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1993-117-02/S0002-9939-1993-1128724-8/S0002-9939-1993-1128724-8.pdf

Reference10 articles.

1. The space 𝐿^{𝜔} and convex topological rings;Arens, Richard;Bull. Amer. Math. Soc.,1946

2. Lecture Notes in Mathematics;Aupetit, Bernard,1979

3. Uniqueness of the uniform norm with an application to topological algebras;Bhatt, S. J.;Proc. Amer. Math. Soc.,1992

4. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 80;Bonsall, Frank F.,1973

5. \bysame, Numerical ranges of operators on normed spaces and of elements of normed algebras, London Math. Soc. Lecture Note Ser., vol. 2, London Math. Soc., Cambridge, 1971.

Cited by 5 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. On Normed Algebras and the Generalized Maligranda–Orlicz Lemma;Symmetry;2023-12-31

2. Orthomodularity and the incompatibility of relativity and quantum mechanics;Quantum Studies: Mathematics and Foundations;2016-10-25

3. A real seminorm with square property is submultiplicative;Indian Journal of Pure and Applied Mathematics;2012-08

4. Bibliography;Topological Algebras with Involution;2005

5. A seminorm with square property is automatically submultiplicative;Proceedings Mathematical Sciences;1998-02