Automatic continuity with application to C*-algebras

1990 ◽  
Vol 107 (2) ◽  
pp. 345-347 ◽  
Author(s):  
Angel Rodriguez Palacios
Keyword(s):  
Banach Algebras ◽  
Direct Consequence ◽  
Automatic Continuity ◽  
Associative Algebras ◽  
C Algebras ◽  
Complete Algebra ◽  
Usual Norm

The fact proved by Cleveland [4], that the topology of any (non-complete) algebra norm on a C*-algebra is stronger than the topology of the usual norm, is reencountered as a direct consequence of a theorem, which we prove in this note, stating that homomorphisms from certain non-complete normed (associative) algebras onto some semisimple Banach algebras are automatically continuous.

scholarly journals Automatic continuity for Banach algebras with finite-dimensional radical

2006 ◽  
Vol 81 (2) ◽  
pp. 279-296 ◽  
Author(s):  
Hung Le Pham
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Automatic Continuity ◽  
Algebraic Condition ◽  
Finite Dimensional ◽  
Complete Algebra

AbstractThe paper [3] proved a necessary algebraic condition for a Banach algebra A with finite-dimensional radical R to have a unique complete (algebra) norm, and conjectured that this condition is also sufficient. We extend the above theorem. The conjecture is confirmed in the case where A is separable and A/R is commutative, but is shown to fail in general. Similar questions for derivations are discussed.

Automatic Continuity of Homomorphisms in Non-associative Banach Algebras

2013 ◽  
Vol 65 (5) ◽  
pp. 989-1004
Author(s):  
C-H. Chu ◽  
M. V. Velasco
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Surjective Homomorphism ◽  
Automatic Continuity ◽  
Normed Algebra ◽  
Associative Algebras ◽  
Rare Element ◽  
Rare Elements

AbstractWe introduce the concept of a rare element in a non-associative normed algebra and show that the existence of such an element is the only obstruction to continuity of a surjective homomorphism from a non-associative Banach algebra to a unital normed algebra with simple completion. Unital associative algebras do not admit any rare elements, and hence automatic continuity holds.

scholarly journals Sur la continuité automatique des épimorphismes dans les☆-algèbres de Banach

2004 ◽  
Vol 2004 (22) ◽  
pp. 1183-1187
Author(s):  
L. Oukhtite ◽  
A. Tajmouati ◽  
Y. Tidli
Keyword(s):  
Banach Algebras ◽  
Automatic Continuity ◽  
Nous Obtenons

Nous étudions les problèmes de continuité automatique dans des algèbres de Banach avec involutions. Nous obtenons aussi des nouveoux résultats concernant☆-idéals des☆-algèbres.We study the automatic continuity problems for Banach algebras with involutions. We also obtain some new results concerning☆-ideals of☆-algebras.

On the Definition of C*-Algebras II

1985 ◽  
Vol 37 (4) ◽  
pp. 664-681 ◽  
Author(s):  
Zoltán Magyar ◽  
Zoltán Sebestyén
Keyword(s):  
Hilbert Space ◽  
Banach Algebra ◽  
Representation Theorem ◽  
Banach Algebras ◽  
Bounded Operators ◽  
Fundamental Representation ◽  
C Algebras ◽  
Definition Of ◽  
Image Position

The theory of noncommutative involutive Banach algebras (briefly Banach *-algebras) owes its origin to Gelfand and Naimark, who proved in 1943 the fundamental representation theorem that a Banach *-algebra with C*-condition(C*)is *-isomorphic and isometric to a norm-closed self-adjoint subalgebra of all bounded operators on a suitable Hilbert space.At the same time they conjectured that the C*-condition can be replaced by the B*-condition.(B*)In other words any B*-algebra is actually a C*-algebra. This was shown by Glimm and Kadison [5] in 1960.

scholarly journals Differential properties of some dense subalgebras of C*-algebras

1994 ◽  
Vol 37 (3) ◽  
pp. 399-422 ◽  
Author(s):  
E. Kissin ◽  
V. S. Shulman
Keyword(s):  
Banach Algebras ◽  
Sufficient Conditions ◽  
C Algebras ◽  
Differentiable Functions ◽  
Differential Properties

The paper studies some classes of dense *-subalgebras B of C*-algebras A whose properties are close to the properties of the algebras of differentiable functions. In terms of a set of norms on B it defines -subalgebras of A and establishes that they are locally normal Q*-subalgebras. If x = x* ∈ B and f(t) is a function on Sp(x), some sufficient conditions are given for f(x) to belong to B. For p = 1, in particular, it is shown that -subalgebras are closed under C∞-calculus. If δ is a closed derivation of A, the algebras D(δp) are -subalgebras of A. In the case when δ is a generator of a one-parameter semigroup of automorphisms of A, it is proved that, in fact, D(δp) are -subalgebras. The paper also characterizes those Banach *-algebras which are isomorphic to subalgebras of C*-algebras.

scholarly journals Perturbation Theory for Quasinilpotents in Banach Algebras

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1163
Author(s):  
Xin Wang ◽  
Peng Cao
Keyword(s):  
Perturbation Theory ◽  
Banach Algebra ◽  
Perturbation Technique ◽  
Banach Algebras ◽  
C Algebras

In this paper, we prove the following result by perturbation technique. If q is a quasinilpotent element of a Banach algebra and spectrum of p + q for any other quasinilpotent p contains at most n values then q n = 0 . Applications to C* algebras are given.

scholarly journals Automatic continuity of $\sigma $-derivations on $C^*$-algebras

2006 ◽  
Vol 134 (11) ◽  
pp. 3319-3327 ◽  
Author(s):  
Madjid Mirzavaziri ◽  
Mohammad Sal Moslehian
Keyword(s):  
Automatic Continuity ◽  
C Algebras
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