Extension theorems for Fredholm and invertibility symbols |
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Authors: | Israel Gohberg Naum Krupnik |
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Affiliation: | (1) School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, 69978 Tel-Aviv, Israel;(2) Department of Mathematics and Computer Science, Bar-Ilan University, 52900 Ramat-Gan, Israel |
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Abstract: | 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. |
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Keywords: | Primary 46K99 Secondary 45E05 |
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