scholarly journals Nearly Jordan -Homomorphisms between Unital -Algebras

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
A. Ebadian ◽  
S. Kaboli Gharetapeh ◽  
M. Eshaghi Gordji
Keyword(s):  
Fixed Points ◽  
Continuous Mapping ◽  
Linear Mapping ◽  
Real Rank ◽  
Real Rank Zero ◽  
Rank Zero ◽  
Unital Algebra ◽  
Jordan Homomorphism ◽  
Jordan Homomorphisms ◽  
Rassias Stability

Let , be two unital -algebras. We prove that every almost unital almost linear mapping : which satisfies for all , all , and all , is a Jordan homomorphism. Also, for a unital -algebra of real rank zero, every almost unital almost linear continuous mapping is a Jordan homomorphism when holds for all (), all , and all . Furthermore, we investigate the Hyers- Ulam-Aoki-Rassias stability of Jordan -homomorphisms between unital -algebras by using the fixed points methods.

Maps preserving Jordan triple product on the self-adjoint elements of C∗-algebras

2016 ◽  
Vol 10 (02) ◽  
pp. 1750022 ◽  
Author(s):  
Ali Taghavi
Keyword(s):  
Triple Product ◽  
Real Rank ◽  
Real Rank Zero ◽  
Rank Zero ◽  
Absolute Value ◽  
C Algebras ◽  
Complex Linear ◽  
Jordan Homomorphisms ◽  
Jordan Triple Product ◽  
Unit Formula

Let [Formula: see text] and [Formula: see text] be two unital [Formula: see text]-algebras with unit [Formula: see text]. It is shown that the mapping [Formula: see text] which preserves arithmetic mean and Jordan triple product is a difference of two Jordan homomorphisms provided that [Formula: see text]. The structure of [Formula: see text] is more refined when [Formula: see text] or [Formula: see text]. Furthermore, if [Formula: see text] is a [Formula: see text]-algebra of real rank zero and [Formula: see text] is additive and preserves absolute value of product, then [Formula: see text] such that [Formula: see text] (respectively, [Formula: see text]) is a complex linear (respectively, antilinear) ∗-homomorphism.

scholarly journals AF FLOWS AND CONTINUOUS SYMMETRIES

2001 ◽  
Vol 13 (12) ◽  
pp. 1505-1528 ◽  
Author(s):  
O. BRATTELI ◽  
A. KISHIMOTO
Keyword(s):  
Symmetry Breaking ◽  
Fixed Points ◽  
Automorphism Groups ◽  
Real Rank ◽  
Continuous Symmetry ◽  
Real Rank Zero ◽  
Rank Zero ◽  
Finite Dimensional ◽  
Continuous Symmetries ◽  
Unital Simple

We consider AF flows, i.e. one-parameter automorphism groups of a unital simple AF C*-algebra which leave invariant the dense union of an increasing sequence of finite-dimensional *-subalgebras, and derive two properties for these; an absence of continuous symmetry breaking and a kind of real rank zero property for the almost fixed points.

scholarly journals Reduction of filtered K-theory and a characterization of Cuntz-Krieger algebras

2014 ◽  
Vol 14 (3) ◽  
pp. 570-613 ◽  
Author(s):  
Sara E. Arklint ◽  
Rasmus Bentmann ◽  
Takeshi Katsura
Keyword(s):  
Primitive Ideal ◽  
Ideal Space ◽  
Real Rank ◽  
Real Rank Zero ◽  
Rank Zero ◽  
K Theory

AbstractWe show that filtered K-theory is equivalent to a substantially smaller invariant for all real-rank-zero C*-algebras with certain primitive ideal spaces—including the infinitely many so-called accordion spaces for which filtered K-theory is known to be a complete invariant. As a consequence, we give a characterization of purely infinite Cuntz–Krieger algebras whose primitive ideal space is an accordion space.

Linear Maps on C*-Algebras Preserving the Set of Operators that are Invertible in

2011 ◽  
Vol 54 (1) ◽  
pp. 141-146
Author(s):  
Sang Og Kim ◽  
Choonkil Park
Keyword(s):  
Real Rank ◽  
Real Rank Zero ◽  
Rank Zero ◽  
Calkin Algebra ◽  
C Algebras ◽  
Linear Maps

AbstractFor C*-algebras of real rank zero, we describe linear maps ϕ on that are surjective up to ideals , and π(A) is invertible in if and only if π(ϕ(A)) is invertible in , where A ∈ and π : → is the quotient map. We also consider similar linear maps preserving zero products on the Calkin algebra.

scholarly journals On the classification of C*-algebras of real rank zero, III: The infinite case

1998 ◽  
pp. 11-72 ◽  
Author(s):  
Ola Bratteli ◽  
George Elliott ◽  
David Evans ◽  
Akitaka Kishimoto
Keyword(s):  
Real Rank ◽  
Real Rank Zero ◽  
Rank Zero ◽  
C Algebras ◽  
Infinite Case
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