scholarly journals Linear maps between $\mathrm{C}^{*}$ -algebras preserving extreme points and strongly linear preservers

2016 ◽  
Vol 10 (3) ◽  
pp. 547-565
Author(s):  
María J. Burgos ◽  
Antonio C. Márquez-García ◽  
Antonio Morales-Campoy ◽  
Antonio M. Peralta
Keyword(s):  
Extreme Points ◽  
C Algebras ◽  
Linear Preservers ◽  
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 rank 2 on the space of alternate matrices and their applications

2004 ◽  
Vol 2004 (63) ◽  
pp. 3409-3417 ◽  
Author(s):  
Chongguang Cao ◽  
Xiaomin Tang
Keyword(s):  
Linear Space ◽  
Linear Preservers ◽  
Linear Maps ◽  
Rank 2

Denote by𝒦n(F)the linear space of alln×nalternate matrices over a fieldF. We first characterize all linear bijective maps on𝒦n(F)(n≥4)preserving rank 2 whenFis any field, and thereby the characterization of all linear bijective maps on𝒦n(F)preserving the max-rank is done whenFis any field except for{0,1}. Furthermore, the linear preservers of the determinant (resp., adjoint) on𝒦n(F)are also characterized by reducing them to the linear preservers of the max-rank whennis even andFis any field except for{0,1}. This paper can be viewed as a supplement version of several related results.

Linear preservers of Hadamard majorization

2016 ◽  
Vol 31 ◽  
pp. 593-609 ◽  
Author(s):  
Sara Motlaghian ◽  
Ali Armandnejad ◽  
Frank Hall
Keyword(s):  
Stochastic Matrix ◽  
Doubly Stochastic Matrix ◽  
Graph Theoretic ◽  
Doubly Stochastic ◽  
Linear Preservers ◽  
Linear Maps ◽  
Term Rank

Let $\textbf{M}_{n }$ be the set of all $n \times n $ realmatrices. A matrix $D=[d_{ij}]\in\textbf{M}_{n } $ with nonnegative entries is called doubly stochastic if $\sum_{k=1}^{n} d_{ik}=\sum_{k=1}^{n} d_{kj}=1$ for all $1\leq i,j\leq n$. For $ X,Y \in \textbf{M}_{n}$ we say that $X$ is Hadamard-majorized by $Y$, denoted by $ X\prec_{H} Y$, if there exists an $n \times n$ doubly stochastic matrix $D$ such that $X=D\circ Y$.In this paper, some properties of$\prec_{H}$ on $\textbf{M}_{n}$ are first obtained, and then the (strong) linear preservers of$\prec_{H}$ on $\textbf{M}_{n }$ are characterized. For $n\geq3$, it is shown that the strong linear preservers of Hadamard majorization on $\textbf{M}_{n}$ are precisely the invertible linear maps on $\textbf{M}_{n}$ which preserve the set of matrices of term rank 1.An interesting graph theoretic connection to the linear preservers of Hadamard majorization is exhibited. A number of examples are also provided in the paper.

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
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