Related papers: On the multiplication of operator-valued c-free ra…

Let (A,phi) be the reduced free product of infinitely many pairs (A_i,phi_i) of C*-algebras with faithful states. Assume that the A_i are not too small, in a specific sense. It is shown that if phi is a trace then K_0(A) is determined…

We construct a formula $\phi$ which axiomatizes non-narrow rectangular grids without using any binary relations other than the grid neighborship relations. As a corollary, we prove that a set $A \subseteq \mathbb{N}$ is a spectrum of a…

In this paper we consider composition operator $C_{\varphi} generated by nonsingular measurable transformation $T$ and multiplication operator $M_u$ generated by measurable function $u$ between two different Orlicz spaces, then we…

In this paper we solve several problems concerning joint similarity to n-tuples of operators in noncommutative varieties in $[B(\cH)^n]_1$ associated with positive regular free holomorphic functions in $n$ noncommuting variables and with…

Let $X$ be a locally compact Hausdorff space, and $A$ be a commutative semisimple Banach algebra over the scalar field $\mathbb{C}$. The correlation between different types of BSE- Banach algebras $A$, and the Banach algebra $C_{0}(X, A)$…

We define a random analytic function $\varphi$ on the unit disc by letting a Gaussian multiplicative measure to be one of its Clark measures. We show that $\varphi$ is almost surely a Blaschke product and we provide rather sharp estimates…

In this paper, we introduce a C*-algebra associated to any substitution (via its Bratteli diagram model). We show that this C*-algebra contains the partial crossed product C*-algebra of the corresponding Bratteli-Vershik system and show…

Let $\varphi$ be a quasi-psh function on a complex manifold $X$ and let $S\subset X$ be a complex submanifold. Then the multiplier ideal sheaves $\mathcal{I}(\varphi|_S)\subset\mathcal{I}(\varphi)|_{S}$ and the complex singularity exponents…

The amalgamated $T$-transform of a non-commutative distribution was introduced by K.~Dykema. It provides a fundamental tool for computing distributions of random variables in Voiculescu's free probability theory. The $T$-transform…

Every positive multilinear map between $C^*$-algebras is separately weak$^*$-continuous. We show that the joint weak$^*$-continuity is equivalent to the joint weak$^*$-continuity of the multiplications of $C^*$-algebras under consideration.…

We study the linear span of commutators of free random variables and show that these are the only quadratic forms which satisfy the following equivalent properties: * preservation free infinite divisibility * free and strong cancellation of…

Let $\mathcal{M}_i$ be a family of $\mathrm{II}_1$-factors, containing a common $\mathrm{II}_1$-subfactor $\mathcal{N}$, such that $[\mathcal{M}_i:\mathcal{N}] \in \mathbb{N}_0$ for all $i$. Furthermore, let $\phi \colon \mathbb{N}_0 \to…

We introduce and characterize, on the Banach lattice valued continuous function space, multiplication operators generating strongly continuous multiplication operator semigroups. Our characterization is the generalization of known results…

In this paper, we discuss hyponormal block Toeplitz operators $T_{\Phi}$ over the vector-valued weighted Bergman space $A_\alpha^2\left(\mathbb{C}^n\right)$. And two conditions about hyponormal block Toeplitz operators $T_{\Phi}$ on…

We present some generalizations of quantum information inequalities involving tracial positive linear maps between $C^*$-algebras. Among several results, we establish a noncommutative Heisenberg uncertainty relation. More precisely, we show…

We develop an approach to noncommutative algebraic geometry ``in the perturbative regime" around ordinary commutative geometry. Let R be a noncommutative algebra and A=R/[R,R] its commutativization. We describe what should be the formal…

We introduce a finite version of free probability for rectangular matrices that amounts to operations on singular values of polynomials. We show that we can replicate the transforms from free probability, and that asymptotically there is…

In this work we study conditional monotone cumulants and additive convolution in the shuffle-algebraic approach to non-commutative probability. We describe c-monotone cumulants as an infinitesimal character and identify the c-monotone…

We introduce C-Algebras of compact Riemann surfaces $\Sigma$ as non-commutative analogues of the Poisson algebra of smooth functions on $\Sigma$. Representations of these algebras give rise to sequences of matrix-algebras for which…

We characterize the strictly increasing symbols $\varphi:\mathbb{N}_0\longrightarrow\mathbb{N}_0$ whose composition operators $C_{\varphi}$ satisfy the Frequent Hypercyclicity Criterion on the little Lipschitz space…