Linear and Multilinear Algebra, ( ISI ), Volume (68), No (8), Year (2018-11) , Pages (1501-1517)

Title : ( Non-linear positive maps between C*-algebras )

Authors: Ali Dadkhah , Mohammad Sal Moslehian ,

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We present some properties of (not necessarily linear) positive maps between C∗-algebras. We first extend the notion of Lieb functions to that of Lieb positive maps between C∗-algebras. Then we give some basic properties and fundamental inequalities related to such maps. Next, we study n-positive maps (n ≥ 2). We show that if for a unital 3-positive map : A −→ B between unital C∗-algebras and some A ∈ A equality (A∗A) = (A) ∗ (A) holds, then (XA) = (X)(A) for all X ∈ A . In addition, we prove that for a certain class of unital positive maps : A −→ B between unital C∗-algebras, the inequality (αA) ≤ α(A) holds for all α ∈ [0, 1] and all positive elements A ∈ A if and only if (0) = 0. Furthermore, we show that if for some α in the unit ball of C or in R+ with |α| = 0, 1, the equality (αI) = αI holds, then is additive on positive elements of A . Moreover, we present a mild condition for a 6-positive map, which ensures its linearity.


, C∗, algebra; n, positive map; Lieb map; superadditive; nonlinear map
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author = {Dadkhah, Ali and Sal Moslehian, Mohammad},
title = {Non-linear positive maps between C*-algebras},
journal = {Linear and Multilinear Algebra},
year = {2018},
volume = {68},
number = {8},
month = {November},
issn = {0308-1087},
pages = {1501--1517},
numpages = {16},
keywords = {C∗-algebra; n-positive map; Lieb map; superadditive; nonlinear map},


%0 Journal Article
%T Non-linear positive maps between C*-algebras
%A Dadkhah, Ali
%A Sal Moslehian, Mohammad
%J Linear and Multilinear Algebra
%@ 0308-1087
%D 2018