scholarly journals New Condition of Automatic Continuity of Dense Range Homomorphisms on Jordan – Banach Algebras

2018 ◽  
Vol 27 (4) ◽  
pp. 146-150
Author(s):  
RUQAYAH N. BALO ◽  
NADIA A. ABDULRAZAQ ◽  
DUAA F. ABDULLAH
Keyword(s):  
Banach Algebras ◽  
Automatic Continuity ◽  
Dense Range

scholarly journals AUTOMATIC CONTINUITY OF n-HOMOMORPHISMS BETWEEN TOPOLOGICAL ALGEBRAS

2011 ◽  
Vol 83 (3) ◽  
pp. 389-400 ◽  
Author(s):  
TAHER G. HONARY ◽  
H. SHAYANPOUR
Keyword(s):  
Banach Algebras ◽  
Automatic Continuity ◽  
Topological Algebras ◽  
Dense Range

AbstractA map θ:A→B between algebras A and B is called n-multiplicative if θ(a1a2⋯an)=θ(a1) θ(a2)⋯θ(an) for all elements a1,a2,…,an∈A. If θ is also linear then it is called an n-homomorphism. This notion is an extension of a homomorphism. We obtain some results on automatic continuity of n-homomorphisms between certain topological algebras, as well as Banach algebras. The main results are extensions of Johnson’s theorem to surjective n-homomorphisms on topological algebras, a theorem due to C. E. Rickart in 1950 to dense range n-homomorphisms on topological algebras and two theorems due to E. Park and J. Trout in 2009 to * -preserving n-homomorphisms on lmc * -algebras.

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.

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.

scholarly journals -Approximately Contractible Banach Algebras

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
M. Momeni ◽  
T. Yazdanpanah ◽  
M. R. Mardanbeigi
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Dense Range ◽  
Approximate Amenability

We investigate -approximate contractibility and -approximate amenability of Banach algebras, which are extensions of usual notions of contractibility and amenability, respectively, where is a dense range or an idempotent bounded endomorphism of the corresponding Banach algebra.

scholarly journals Automatic continuity of certain isomorphisms between regular Banach function algebras

1997 ◽  
Vol 39 (3) ◽  
pp. 333-343 ◽  
Author(s):  
Juan J. Font
Keyword(s):  
Banach Algebras ◽  
Automatic Continuity ◽  
Linear Map ◽  
Function Algebras ◽  
Commutative Banach Algebras ◽  
Disjointness Preserving ◽  
Banach Function Algebras

AbstractLet A and B be regular semisimple commutative Banach algebras; that is to say, regular Banach function algebras. A linear map T denned from A into B is said to be separating or disjointness preserving if f.g = 0 implies Tf.Tg = 0, for all f, g ∈ A In this paper we prove that if A satisfies Ditkin's condition then a separating bijection is automatically continuous and its inverse is separating. If also B satisfies Ditkin's condition, then it induces a homeomorphism between the structure spaces of A and B.

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.

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