Extension theorems for Fredholm and invertibility symbols

Israel Gohberg, Naum Krupnik

Research output: Contribution to journalArticlepeer-review

32 Scopus citations


This paper is a continuation of [GK3] where the theory of Invertibility Symbol in Banach algebras was developed. In the present paper we generalize these results for the case when the Invertibility Symbol is defined on a subalgebra of the Banach algebras. The difficulty which arises here in this more general case is connected with the fact that some elements of the subalgebra may have the inverses which do not belong to the subalgebra. This generalization of the theory allows us to study the Fredholm Symbols of linear operators. Applications to subalgebras generated by two idempotents and to algebras generated by singular integral operators are presented.

Original languageEnglish
Pages (from-to)514-529
Number of pages16
JournalIntegral Equations and Operator Theory
Issue number4
StatePublished - Dec 1993


  • MSC: Primary 46K99, Secondary 45E05


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