scholarly journals Linear maps on C ⁎ -algebras which are derivations or triple derivations at a point

2018 ◽  
Vol 538 ◽  
pp. 1-21 ◽  
Author(s):  
Ahlem Ben Ali Essaleh ◽  
Antonio M. Peralta
Keyword(s):  
C Algebras ◽  
Linear Maps

Positive Linear Maps on C*-Algebras

1972 ◽  
Vol 24 (3) ◽  
pp. 520-529 ◽  
Author(s):  
Man-Duen Choi
Keyword(s):  
Vector Spaces ◽  
Complex Numbers ◽  
Complex Matrices ◽  
Completely Positive ◽  
C Algebras ◽  
Linear Maps ◽  
Positive Linear Maps

The objective of this paper is to give some concrete distinctions between positive linear maps and completely positive linear maps on C*-algebras of operators.Herein, C*-algebras possess an identity and are written in German type . Capital letters A, B, C stand for operators, script letters for vector spaces, small letters x, y, z for vectors. Capital Greek letters Φ, Ψ stand for linear maps on C*-algebras, small Greek letters α, β, γ for complex numbers.We denote by the collection of all n × n complex matrices. () = ⊗ is the C*-algebra of n × n matrices over .

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 Linear maps on *-algebras acting on orthogonal elements like derivations or anti-derivations

Filomat ◽  
2018 ◽  
Vol 32 (13) ◽  
pp. 4543-4554 ◽  
Author(s):  
H. Ghahramani ◽  
Z. Pan
Keyword(s):  
Linear Map ◽  
Unital Algebra ◽  
C Algebras ◽  
Orthogonality Conditions ◽  
Linear Maps ◽  
Unital Simple

Let U be a unital *-algebra and ? : U ? U be a linear map behaving like a derivation or an anti-derivation at the following orthogonality conditions on elements of U: xy = 0, xy* = 0, xy = yx = 0 and xy* = y*x = 0. We characterize the map ? when U is a zero product determined algebra. Special characterizations are obtained when our results are applied to properly infinite W*-algebras and unital simple C*-algebras with a non-trivial idempotent.

scholarly journals Linear maps preserving ideals of C$^{*}$-algebras

2003 ◽  
Vol 131 (11) ◽  
pp. 3441-3446 ◽  
Author(s):  
Jianlian Cui ◽  
Jinchuan Hou
Keyword(s):  
C Algebras ◽  
Linear Maps

Tracial Positive Linear Maps of C ∗ -Algebras

1983 ◽  
Vol 87 (1) ◽  
pp. 57
Author(s):  
Man-Duen Choi ◽  
Sze-Kai Tsui
Keyword(s):  
C Algebras ◽  
Linear Maps ◽  
Positive Linear Maps

scholarly journals TRACIAL EQUIVALENCE FOR $C^*$-ALGEBRAS AND ORBIT EQUIVALENCE FOR MINIMAL DYNAMICAL SYSTEMS

2005 ◽  
Vol 48 (3) ◽  
pp. 673-690
Author(s):  
Huaxin Lin
Keyword(s):  
Dynamical Systems ◽  
Crossed Products ◽  
Rank Zero ◽  
C Algebras ◽  
Orbit Equivalent ◽  
Linear Maps ◽  
Positive Linear Maps ◽  
Tracial Topological Rank ◽  
Minimal Dynamical Systems ◽  
Cantor Minimal Systems

AbstractWe introduce the notion of tracial equivalence for $C^*$-algebras. Let $A$ and $B$ be two unital separable $C^*$-algebras. If they are tracially equivalent, then there are two sequences of asymptotically multiplicative contractive completely positive linear maps $\phi_n:A\to B$ and $\psi_n:B\to A$ with a tracial condition such that $\{\phi_n\circ\psi_n\}$ and $\{\psi_n\circ\phi_n\}$ are tracially approximately inner. Let $A$ and $B$ be two unital separable simple $C^*$-algebras with tracial topological rank zero. It is proved that $A$ and $B$ are tracially equivalent if and only if $A$ and $B$ have order isomorphic ranges of tracial states. For the Cantor minimal systems $(X_1,\sigma_1)$ and $(X_2,\sigma_2)$, using a result of Giordano, Putnam and Skau, we show that two such dynamical systems are (topological) orbit equivalent if and only if the associated crossed products $C(X_1)\times_{\sigma_1}\mathbb{Z}$ and $C(X_2)\times_{\sigma_2}\mathbb{Z}$ are tracially equivalent.

scholarly journals Linear maps preserving regularity in C∗-algebras

2009 ◽  
Vol 53 (3) ◽  
pp. 899-914
Author(s):  
Abdellatif Bourhim ◽  
María Burgos
Keyword(s):  
C Algebras ◽  
Linear Maps

scholarly journals Contractive linear maps on $C^*$-algebras.

1976 ◽  
Vol 22 (4) ◽  
pp. 361-366 ◽  
Author(s):  
Richard I. Loebl
Keyword(s):  
C Algebras ◽  
Linear Maps
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