scholarly journals Groups of invertible elements of Banach algebras

1973 ◽  
Vol 79 (1) ◽  
pp. 82-85 ◽  
Author(s):  
Yvonne Yuen
Keyword(s):  
Banach Algebras ◽  
Invertible Elements

scholarly journals Invertibility-preserving maps ofC∗-algebras with real rank zero

2005 ◽  
Vol 2005 (6) ◽  
pp. 685-689 ◽  
Author(s):  
Istvan Kovacs
Keyword(s):  
Banach Algebras ◽  
Real Rank ◽  
Real Rank Zero ◽  
Rank Zero ◽  
Linear Map ◽  
Linear Bijection ◽  
Jordan Isomorphism ◽  
Invertible Elements

In 1996, Harris and Kadison posed the following problem: show that a linear bijection betweenC∗-algebras that preserves the identity and the set of invertible elements is a Jordan isomorphism. In this paper, we show that ifAandBare semisimple Banach algebras andΦ:A→Bis a linear map ontoBthat preserves the spectrum of elements, thenΦis a Jordan isomorphism if eitherAorBis aC∗-algebra of real rank zero. We also generalize a theorem of Russo.

ON IDEALS OF GENERALISED INVERTIBLE ELEMENTS IN BANACH ALGEBRAS

2005 ◽  
Vol 105A (2) ◽  
pp. 1-10
Author(s):  
R. M. Brits ◽  
L. Lindeboom ◽  
H. Raubenheimer
Keyword(s):  
Banach Algebras ◽  
Invertible Elements

scholarly journals Regular Fréchet–Lie Groups of Invertible Elements in Some Inverse Limits of Unital Involutive Banach Algebras

1995 ◽  
Vol 2 (4) ◽  
pp. 425-444
Author(s):  
Jean Marion ◽  
Thierry Robart
Keyword(s):  
Differential Geometry ◽  
Lie Groups ◽  
Wide Class ◽  
Fundamental Theorem ◽  
Banach Algebras ◽  
Inverse Limits ◽  
Topological Algebras ◽  
Infinite Dimensional ◽  
Dimensional Version ◽  
Invertible Elements

Abstract We consider a wide class of unital involutive topological algebras provided with a C*-norm and which are inverse limits of sequences of unital involutive Banach algebras; these algebras are taking a prominent position in noncommutative differential geometry, where they are often called unital smooth algebras. In this paper we prove that the group of invertible elements of such a unital solution smooth algebra and the subgroup of its unitary elements are regular analytic Fréchet–Lie groups of Campbell–Baker–Hausdorff type and fulfill a nice infinite-dimensional version of Lie's second fundamental theorem.

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