Related papers: Brown measures of sets of commuting operators in a…

Whether an almost-commuting pair of operators must be close to a commuting pair is a central question in operator and matrix theory. We investigate this problem for pairs of $C^*$-subalgebras $\mathcal{A}$ and $\mathcal{B}$ of…

A major open question in the theory of Toeplitz operator on the Bergman space of the unit disk of the complex plane is to fully characterize the set of all Toeplitz operators that commute with a given one. In [2], the second author…

Let $T\colon H\to H$ be a bounded operator on Hilbert space. We say that $T$ has a polygonal type if there exists an open convex polygon $\Delta\subset {\mathbb D}$, with $\overline{\Delta}\cap{\mathbb T}\neq\emptyset$, such that the…

We use subordination functions perspective to reformulate Haagerup--Schultz's approach for the Brown measure of $R$-diagonal operators. This allows us to simplify the original argument and find a connection with the other approach due to…

We investigate small deviation properties of Gaussian random fields in the space $L_q(\R^N,\mu)$ where $\mu$ is an arbitrary finite compactly supported Borel measure. Of special interest are hereby "thin" measures $\mu$, i.e., those which…

Suppose that $\omega$ is a radial weight on the unit disk that satisfies both forward and reverse doubling conditions. Using Carleson measures and $T1$-type conditions, we obtain necessary and sufficient conditions of the positive Borel…

The DT-operators are introduced, one for every pair (\mu,c) consisting of a compactly supported Borel probability measure \mu on the complex plane and a constant c>0. These are operators on Hilbert space that are defined as limits in…

Let (M,\mu) be a sigma-finite measure space. Let (T_t) be a semigroup of positive preserving maps on (M,\mu) with standard assumptions. We prove a H_1-BMO duality theory with assumptions only on T_t. The BMO is defined as spaces of…

A particular case of results from [K2] is as follows. Let the unitary asymptote of a contraction $T$ contain the bilateral shift (of finite or infinite multiplicity). Then there exists an invariant subspace $\mathcal M$ of $T$ such that…

Let $H$ be an infinite dimensional separable Hilbert space and $B(H)$ the C*-algebra of bounded operators on $H.$ Suppose that $T_1,T_2,..., T_n$ are self-adjoint operators in $B(H).$ We show that, if commutators $[T_i, T_j]$ are…

Let $(X,\mathcal{A}, \mu)$ be a probability measure space and let $T_i,$ $1\leq i\leq H,$ be commuting invertible measure preserving transformations on this measure space. We prove the following pointwise results; The averages…

Let $[b,\mathcal T_\alpha]~(0\leq\alpha<n)$ be the commutators generated by $BMO(\mathbb R^n)$ functions and a class of sublinear operators satisfying certain size conditions. The aim of this paper is to study the endpoint estimates of…

We consider a family $b_{s,\tau}$ of free multiplicative Brownian motions labeled by a real variance parameter $s$ and a complex covariance parameter $\tau$. We then consider the element $xb_{s,\tau}$, where $x$ is non-negative and freely…

Suppose that $X_{1}$ and $X_{2}$ are two $*$-free (generally unbounded) random variables with Brown measures $\mu_{X_{1}}$ and $\mu_{X_{2}}$, respectively. Using properties of classical free additive convolutions, we develop a method for…

Let $S^1$ be the stopping time space and $\mathcal{B}_1(S^1)$ be the Baire-1 elements of the second dual of $S^1$. To each element $x^{**}$ in the space $\mathcal{B}_1(S^1)$ we associate a positive Borel measure $\mu_{x^{**}}$ on the Cantor…

We discuss a notion, originally introduced by Aleman in one variable, of Dirichlet-type space $\mathcal D(\mu_1,\mu_2)$ on the unit bidisc $\mathbb D^2,$ with superharmonic weights related to finite positive Borel measures $\mu_1,\mu_2$ on…

A weighted sums of squares decomposition of positive Borel measurable functions on a bounded Borel subset of the Euclidean space is obtained via duality from the spectral theorem for tuples of commuting self-adjoint operators. The analogous…

Given two Hermitian matrices, $A$ and $B$, we introduce a new type of spectral measure, a $\textit{tracial joint spectral measure}$ $\mu_{A, B}$ on the plane. Existence of this measure implies the following two results: 1) any…

Let $T = (T_1, \ldots, T_n)$ be a commuting tuple of bounded linear operators on a Hilbert space $\mathcal{H}$. The multiplicity of $T$ is the cardinality of a minimal generating set with respect to $T$. In this paper, we establish an…

We investigate monotone operator functions of several variables under a trace or a trace-like functional. In particular, we prove the inequality \tau(x_1... x_n)\le\tau(y_1... y_n) for a trace \tau on a C^*-algebra and abelian n-tuples…