On a Generalization of the Gelfand Transform to Non-commutative Banach Algebras
Author | : Ivan E. Guzman |
Publisher | : |
Total Pages | : 64 |
Release | : 2013 |
ISBN-10 | : OCLC:871701676 |
ISBN-13 | : |
Rating | : 4/5 (76 Downloads) |
Download or read book On a Generalization of the Gelfand Transform to Non-commutative Banach Algebras written by Ivan E. Guzman and published by . This book was released on 2013 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Gelfand theory for an arbitrary Banach algebra A is a pair (G, A), such that: A is a C*-algebra and G : A -> A is an algebra homomorphism; G induces a bijection between the set of maximal modular left ideals of A and the set of maximal modular left ideals of A; and for every maximal modular left ideal L of A, the map G[subscript L] : A/G[superscript -1](L) -> A/L induced by G has dense range. We prove that if A is a postliminal C*-algebra with Gelfand theory (G, A), then no proper C*-subalgebra of A contains GA. We also show that if J is an ideal of a Banach algebra A such that A/J and J both have Gelfand theories, then A also has a Gelfand theory if we impose some conditions on J and on its Gelfand theory.