caa a22 4500 469043318 CHVBK 20180323132817.0 cr unu---uuuuu 170328e19921101xx s 000 0 eng 10.1007/BF01203124 doi (NATIONALLICENCE)springer-10.1007/BF01203124 Extension theorems for Invertibility Symbols in Banach algebras [Elektronische Daten] [Israel Gohberg, Naum Krupnik] 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. Birkhäuser Verlag, 1992 Primary 46K99 nationallicence Secondary 45E05 nationallicence Gohberg Israel School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, 69978, Tel-Aviv, Israel aut Krupnik Naum School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, 69978, Tel-Aviv, Israel aut Integral Equations and Operator Theory Birkhäuser-Verlag 15/6(1992-11-01), 991-1010 0378-620X 15:6<991 1992 15 20 https://doi.org/10.1007/BF01203124 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01203124 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Gohberg Israel School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, 69978, Tel-Aviv, Israel aut NATIONALLICENCE 700 1- Krupnik Naum School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, 69978, Tel-Aviv, Israel aut NATIONALLICENCE 773 0- Integral Equations and Operator Theory Birkhäuser-Verlag 15/6(1992-11-01), 991-1010 0378-620X 15:6<991 1992 15 20 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer