Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

BANACH ALGEBRAS WITH LARGE GROUPS OF UNITARY ELEMENTS

BANACH ALGEBRAS WITH LARGE GROUPS OF UNITARY ELEMENTS AbstractWe study unitary Banach algebras, as defined by M. L. Hansen and R. V. Kadison in 1996, as well as some related concepts like maximal or uniquely maximal Banach algebras. We show that a norm-unital Banach algebra is uniquely maximal if and only if it is unitary and has minimality of the equivalent norm. We prove that every unitary semisimple commutative complex Banach algebra has a conjugate-linear involution mapping each unitary element to its inverse, and that, endowed with such an involution, becomes a hermitian -algebra. The possibility of removing the requirement of commutativity in the above statement is also considered. The paper concludes by translating to real algebras some results previously known in the complex case. In particular, we show that every maximal semisimple finite-dimensional real Banach algebra is isometrically isomorphic to a real C-algebra. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The Quarterly Journal of Mathematics Oxford University Press

Loading next page...
 
/lp/oxford-university-press/banach-algebras-with-large-groups-of-unitary-elements-PF0w10cfoQ

References (53)

Publisher
Oxford University Press
Copyright
© Published by Oxford University Press.
ISSN
0033-5606
eISSN
1464-3847
DOI
10.1093/qmath/ham004
Publisher site
See Article on Publisher Site

Abstract

AbstractWe study unitary Banach algebras, as defined by M. L. Hansen and R. V. Kadison in 1996, as well as some related concepts like maximal or uniquely maximal Banach algebras. We show that a norm-unital Banach algebra is uniquely maximal if and only if it is unitary and has minimality of the equivalent norm. We prove that every unitary semisimple commutative complex Banach algebra has a conjugate-linear involution mapping each unitary element to its inverse, and that, endowed with such an involution, becomes a hermitian -algebra. The possibility of removing the requirement of commutativity in the above statement is also considered. The paper concludes by translating to real algebras some results previously known in the complex case. In particular, we show that every maximal semisimple finite-dimensional real Banach algebra is isometrically isomorphic to a real C-algebra.

Journal

The Quarterly Journal of MathematicsOxford University Press

Published: Jun 18, 2007

There are no references for this article.