Related papers: Finite rank Bergman-Toeplitz and Bargmann-Toeplitz…
We study the weighted compactness and boundedness of Toeplitz operators on the Fock spaces. Fix $\alpha>0$. Let $T_{\varphi}$ be the Toeplitz operator on the Fock space $F^2_{\alpha}$ over $\mathbb{C}^n$ with symbol $\varphi\in L^{\infty}$.…
We study mapping properties of Toeplitz operators associated to a finite positive Borel measure on a bounded strongly pseudoconvex domain D in n complex variables. In particular, we give sharp conditions on the measure ensuring that the…
In this note we describe centralizers of Toeplitz operators with polynomial symbols on the Bergman space. As a consequence it is shown that if an element of the norm closed algebra generated by all Toeplitz operators commutes with a…
In this paper we present some consequences of the description of matrix representations of asymmetric truncated Toeplitz operators acting between finite-dimensional model spaces. In particular, we prove that these operators can be…
We obtain a Szeg\"o limit theorem for a family of Toeplitz operators defined on the weighted Bergman space of the unit ball $\mathbb{B}_{n}$. The symbols of these operators are supported on some isotropic or co-isotropic submanifold $\Gamma…
We prove a version of the Lefschetz fixed point theorem for multivalued maps $F:X\multimap X$ in which $X$ is a finite $T_0$ space.
Sharp upper and lower bounds for the second and third order Hermitian-Toepilitz determinants are obtained for some generalized subclasses of starlike and convex functions. Applications of these results are also discussed for several widely…
This work provides closed-form solutions and minimum achievable errors for a large class of low-rank approximation problems in Hilbert spaces. The proposed theorem generalizes to the case of bounded linear operators the previous results…
The results in the paper are related to the classification problem for invariant subspaces of multiplication operators in several variables. The main results consist of characterizations, in the two dimensional case, of ideals of…
We derive in this preprint the exact up to multiplicative constant non-asymptotical estimates for the norms of some non-linear in general case operators, for example, the so-called maximal functional operators, in two probabilistic…
This paper studies a new maximal operator introduced by Hyt\"onen, McIntosh and Portal in 2008 for functions taking values in a Banach space. The L^p-boundedness of this operator depends on the range space; certain requirements on type and…
We show that truncated Toeplitz operators are characterized by a collection of complex symmetries. This was conjectured by Klis-Garlicka, Lanucha, and Ptak, and proved by them in some special cases.
We study a class of rotation invariant determinantal ensembles in the complex plane; examples include the eigenvalues of Gaussian random matrices and the roots of certain families of random polynomials. The main result is a criteria for a…
The determination of the maximal ranks of a set of a given type of tensors is a basic problem both in theory and application. In statistical applications, the maximal rank is related to the number of necessary parameters to be built in a…
Semi-infinite forms on the moduli spaces of genus-zero Riemann surfaces with punctures and local coordinates are introduced. A partial operad for semi-infinite forms is constructed. Using semi-infinite forms and motivated by a partial…
Truncated Toeplitz operators are compressions of Toeplitz operators on model spaces; they have received much attention in the last years. This survey article presents several recent results, which relate boundedness, compactness, and…
Rank invariants are a parametrized version of Betti numbers of a space multi-filtered by a continuous vector-valued function. In this note we give a sufficient condition for their finiteness. This condition is sharp for spaces embeddable in…
We present some extensions of Bernstein's concentration inequality for random matrices. This inequality has become a useful and powerful tool for many problems in statistics, signal processing and theoretical computer science. The main…
By means of fixed point index theory for multi-valued maps, we provide an analogue of the classical Birkhoff--Kellogg Theorem in the context of discontinuous operators acting on affine wedges in Banach spaces. Our theory is fairly general…
For $\mathbb{B}^n$ the $n$-dimensional unit ball and $D_n$ its Siegel unbounded realization, we consider Toeplitz operators acting on weighted Bergman spaces with symbols invariant under the actions of the maximal Abelian subgroups of…