Extension theorems for Invertibility Symbols in Banach algebras |
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Authors: | Israel Gohberg Naum Krupnik |
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Institution: | (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: | 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. |
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Keywords: | Primary 46K99 Secondary 45E05 |
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