On Banach Algebras Generated by Two Idempotents

Ysette Weiss

A chapter in Algebraic Methods in Operator Theory, 1994, pp 90-97 from Springer

Abstract: Abstract A matricial analogue of the Gel’fand map is constructed for the elements of a unital Banach algebra generated by two idempotents. For commutative unital algebras, the Gel’fand map realizes an imbedding into the algebra of all continuous functions on a well-defined set, namely the space of maximal ideals. Analogously, a semisimple algebra can be shown to be isomorphic to a subalgebra of all continuous 2 x 2 matrix-valued functions on a compact set with possible poles of order two at two points, and continuous trace. Conditions for the semisimplicity of the algebra are given, as well as a formula for the computation of the spectral radii of its elements.

Date: 1994
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-0255-4_11

Ordering information: This item can be ordered from
http://www.springer.com/9781461202554

DOI: 10.1007/978-1-4612-0255-4_11

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().