Related papers: Gr\"uss type inequalities for positive linear maps…

Let $\Omega$ be a class of ${\rm C^*}$-algebras. In this paper, we study a class of not necessarily unital generalized tracial approximation ${\rm C^*}$-algebras, and the class of simple ${\rm C^*}$-algebras which can be generally tracially…

In this paper, we generalize some matrix inequalities involving matrix power and Karcher means of positive definite matrices. Among other inequalities, it is shown that if ${\mathbb A}=(A_{1},...,A_{n})$ is a $n$-tuple of positive definite…

Let A be a C*-algebra and d from A into A** be a continuous linear map. We assume that d acts like derivation or anti-derivation at orthogonal elements for several types of orthogonality conditions such as ab=0, ab*=0, ab=ba=0 and…

For unital $C^*$-algebras $A$ and $B$, we completely characterize the isometric ($*$-) automorphisms of their Banach space projective tensor product $A\otimes^\gamma B$. This leads to the characterization of inner and outer isometric…

Let $C$ and $A$ be two unital separable amenable simple C*-algebras with tracial rank no more than one. Suppose that $C$ satisfies the Universal Coefficient Theorem and suppose that $\phi_1, \phi_2: C\to A$ are two unital monomorphisms. We…

In an attempt to propose more general conditions for decoherence to occur, we study spectral and ergodic properties of unital, completely positive maps on not necessarily unital $C^*$-algebras, with a particular focus on gapped maps for…

Inspired by the recent work of Bekka, we study two reasonable analogues of property (T) for not necessarily unital C*-algebras. The stronger one of the two is called ``property (T)'' and the weaker one is called ``property (T_{e})''. It is…

We define variants of Pisier's similarity degree for unital C*-algebras and use direct integral theory to obtain new results. We prove that if every II$_{1}$ factor representation of a separable C*-algebra $\mathcal{A}$ has property…

Let $C=C(X)$ be the unital $C^*$-algebra of all continuous functions on a finite CW complex $X$ and let $A$ be a unital simple $C^*$-algebra with tracial rank at most one. We show that two unital monomorphisms $\phi, \psi: C\to A$ are…

Let $A$ and $B$ be C$^*$-algebras. A linear map $T:A\to B$ is said to be a $^*$-homomorphism at an element $z\in A$ if $a b^*=z$ in $A$ implies $T (a b^*) =T (a) T (b)^* =T(z)$, and $ c^* d=z$ in $A$ gives $T (c^* d) =T (c)^* T (d) =T(z).$…

Using the natural duality between linear functionals on tensor products of C*-algebras with the trace class operators on a Hilbert space H and linear maps of the C*-algebra into B(H), we give two characterizations of separability, one…

For a positive linear map F and a normal matrix N, we show that |F(N)| is bounded by some simple linear combinations in the unitary orbit of F(|N|). Several elegant sharp inequalities are derived, especially for the Schur product.

Let $A \subset C$ and $B \subset D$ be unital inclusions of unital $C^*$-algebras. Let ${}_A \mathbf{B}_A (C, A)$ (resp. ${}_B \mathbf{B}_B (D, B)$) be the space of all bounded $A$-bimodule (resp. $B$-bimodule) linear maps from $C$ (resp.…

We establish some operator versions of Bellman's inequality. In particular, we prove that if $\Phi: \mathbb{B}(\mathscr{H}) \to \mathbb{B}(\mathscr{K})$ is a unital positive linear map, $A,B \in \mathbb{B}(\mathscr{H})$ are contractions,…

We study holomorphic maps between C$^*$-algebras $A$ and $B$. When $f:B_A (0,\varrho) \longrightarrow B$ is a holomorphic mapping whose Taylor series at zero is uniformly converging in some open unit ball $U=B_{A}(0,\delta)$ and we assume…

Let $\mathcal{A}$ and $\mathcal{B}$ be two $C^{*}$-algebras such that $\mathcal{B}$ is prime. In this paper, we investigate the additivity of map $\Phi$ from $\mathcal{A}$ onto $\mathcal{B}$ that are bijective unital and satisfies…

We consider the convex set of ( unital ) positive ( completely ) maps from a $C^*$ algebra $\cla$ to a von-Neumann sub-algebra $\clm$ of $\clb(\clh)$, the algebra of bounded linear operators on a Hilbert space $\clh$ and study its extreme…

Let $\Phi$ be a unital completely positive (UCP) map on the space of operators on some Hilbert space. We assume that $\Phi$ is $\eta$-idempotent, namely, $\|\Phi^2-\Phi\|_{\mathrm{cb}} \le\eta$, and construct an associated…

In a unital C*-algebra with a faithful trace functional $\tau$, the set $D_\tau(A)$ of positive $\rho\in A$ of trace \tau(\rho)=1 is an algebraic analogue of the space of density matrices (the set of all positive matrices of a fixed…

We study the uniform property $\Gamma$ for separable simple $C^*$-algebras which have quasitraces and may not be exact. We show that a stably finite separable simple $C^*$-algebra $A$ with strict comparison and uniform property $\Gamma$ has…