Extension theorems for Invertibility Symbols in Banach algebras

Israel Gohberg, Naum Krupnik

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

Abstract

Necessary and sufficient conditions are found for the possibility of an extension of Invertibility Symbols from a dense subalgebra to its closure. It is proved that such an extension is possible if and only if the closure does not have any Kakutani elements. The extension of Invertibility Symbols from a Banach algebra to the matrix-valued case is also considered. Algebras with Polynomial Identities play an important role here. Applications to algebras generated by two idempotents and to algebras generated by singular integral operators are suggested.

Original languageEnglish
Pages (from-to)991-1010
Number of pages20
JournalIntegral Equations and Operator Theory
Volume15
Issue number6
DOIs
StatePublished - Nov 1992

Keywords

  • MSC: Primary 46K99, Secondary 45E05

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