scholarly journals Isolated spectral points and Koliha-Drazin invertible elements in quotient Banach algebras and homomorphism ranges

2015 ◽  
Vol 115A (2) ◽  
pp. 1-15
Author(s):  
Enrico Boasso
2005 ◽  
Vol 2005 (6) ◽  
pp. 685-689 ◽  
Author(s):  
Istvan Kovacs

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.


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

1995 ◽  
Vol 2 (4) ◽  
pp. 425-444
Author(s):  
Jean Marion ◽  
Thierry Robart

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.


Sign in / Sign up

Export Citation Format

Share Document