Symmetrization of the symbol in Banach algebras generated by idempotents

Naum Krupnik

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3 Scopus citations

Abstract

It is known [2] that a Banach algebra A generated by 2N idempotents with relations (1),(2) is an algebra with matrix symbol of order 2N. This symbol is completely and explicitly denned via the spectrums of two (indicator) elements (3) and (5). But in the case when double-struck A is a c*-algebra. the symbol constructed in [2] is not symmetric. Moreover in order to construct a symmetric symbol, one needs some additional information about the algebra A, even for the case when pj = p*j (j = 1, ..., 2N). These additional conditions and the explicit form of symmetric symbol are described in this paper.

Original languageEnglish
Pages (from-to)470-481
Number of pages12
JournalIntegral Equations and Operator Theory
Volume31
Issue number4
DOIs
StatePublished - Aug 1998

Bibliographical note

Funding Information:
1This research was supported by the Israel Science Foundation founded by the Israel Academy of Sciences and Humanities.

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