Related papers: Mean Lipschitz spaces and a generalized Hilbert op…

We generalize the notion of $m$-isometric operator tuples on Hilbert spaces in a natural way to normed spaces. This is done by defining a tuple analogue of $(m,p)$-isometric operators, so-called $(m,p)$-isometric operator tuples. We then…

The aim of this article is to study effective Reifenberg theorems for measures in a Hilbert or Banach space. For Hilbert spaces, we see all the results from $\mathbb{R}^n$ continue to hold with no additional restrictions. For a general…

Let $\mathcal{H}$ be a right quaternionic Hilbert space and let $T$ be a quaternionic normal operator with the domain $\mathcal{D}(T) \subset \mathcal{H}$. Then for a fixed unit imaginary quaternion $m$, there exists a Hilbert basis…

It is a classic result in modal logic that the category of modal algebras is dually equivalent to the category of descriptive frames. The latter are Kripke frames equipped with a Stone topology such that the binary relation is continuous.…

The main goal of this work is to examine the structure of normal Hausdorff operators on $\mathbb{R}^n$. We show that normal Hausdorff operator in $L^2(\mathbb{R}^n)$ is unitary equivalent to the operator of multiplication by some…

We consider an action of the circle group, T on a von Neumann algebra, M. Similarly to the case when the algebra of essentially bounded functions on T is acted upon by translations, we define the generalized Hardy subspace of H,where H is…

Let $\varphi$ be a normal state on the algebra $B(H)$ of all bounded operators on a Hilbert space $H$, $f$ a strictly positive, continuous function on $(0, \infty)$, and let $g$ be a function on $(0, \infty)$ defined by $g(t) =…

Let $A$ be a normal operator in a Hilbert space $\mathcal{H}$, and let $\mathcal{G} \subset \mathcal{H}$ be a countable set of vectors. We investigate the relations between $A$, $\mathcal{G}$ , and $L$ that makes the system of iterations…

For a positive finite Borel measure $\mu$ compactly supported in the complex plane, the space $\mathcal{P}^2(\mu)$ is the closure of the analytic polynomials in the Lebesgue space $L^2(\mu)$. According to Thomson's famous result, any space…

We focus on Borel measures that have a globally subanalytic density function. We prove, given such a measure $\mu$ on a set $A$ and a globally subanalytic mapping $\Phi:A\to \Omega$, with $\Omega$ bounded open subset of $\mathbb{R}^n$, a…

An extension of Marcinkiewicz Interpolation Theorem, allowing intermediate spaces of Orlicz type, is proved. This generalization yields a necessary and sufficient condition so that every quasilinear operator, which maps the set, $S(X,\mu)$,…

This is basically a summary of [Mu]. The focus of the paper is the explicit computation of Hecke operators for period functions. In particular we compute the matrix representations of the 2nd Hecke operator on period functions for the full…

We analyze the relationship between Borel measures and continuous linear functionals on the space $\mathrm{Lip}_0(M)$ of Lipschitz functions on a complete metric space $M$. In particular, we describe continuous functionals arising from…

Let $\Omega$ be a subdomain of $\mathbb{C}$ and let $\mu$ be a positive Borel measure on $\Omega$. In this paper, we study the asymptotic behavior of the eigenvalues of compact Toeplitz operator $T_\mu$ acting on Bergman spaces on $\Omega$.…

A quasi-Hermitian operator is an operator that is similar to its adjoint in some sense, via a metric operator, i.e., a strictly positive self-adjoint operator. Whereas those metric operators are in general assumed to be bounded, we analyze…

Making use of the simple fact that all separable complex Hilbert spaces of given dimension are isomorphic, we show that there are just six basic ways to define generalized coordinate operators in Quantum Mechanics. In each case a…

Let $\mathcal{H}$ be a Hilbert space, and let $K(\mathcal{H})$ be the $C^*$-algebra of compact operators on $\mathcal{H}$. In this paper, we present some characterizations of the norm-parallelism for elements of a Hilbert…

We present complete classifications of Toeplitz + Hankel operators on vector-valued Hardy spaces and classify paired operators on $L^2(\mathbb{T})$. We also study the latter class through the lens of inner functions on the disc.

This is a tutorial introduction to the functional analysis mathematics needed in many physical problems, such as in waves in continuous media. Functional analysis takes us beyond finite matrices, allowing us to work with infinite sets of…

We study composition operators of characteristic zero on weighted Hilbert spaces of Dirichlet series. For this purpose we demonstrate the existence of weighted mean counting functions associated with the Dirichlet series symbol, and provide…