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In this peaper we stady certain Bessel sequences $\left\{f_k\right\}_{k=1}^{\infty}$ in Hilbert C*- modules $\mathcal{H}$ for which operator $S$ defined by \ref{eq2} is of the form $\mathcal{T}+\xi I$, for some real number $\xi$ and a…

We characterize the reproducing kernel Hilbert spaces whose elements are $p$-integrable functions in terms of the boundedness of the integral operator whose kernel is the reproducing kernel. Moreover, for $p=2$ we show that the spectral…

Hilbert(ian) A-modules over finite von Neumann algebras A with a faithful normal trace state (from global analysis) and Hilbert W*-modules over A (from operator algebra theory) are compared, and a categorical equivalence is established. The…

We study curvature functionals for immersed 2-spheres in non-compact, three-dimensional Riemannian manifold $(M,h)$ without boundary. First, under the assumption that $(M,h)$ is the euclidean 3-space endowed with a semi-perturbed metric…

For a bounded open set Omega in a complete oriented Riemannian n-manifold and a positive finite Borel measure mu with support contained in Omega, we define an associated Krein-Feller operators (or Laplacian) Delta_mu by assuming the…

We provide necessary and sufficient conditions for a Hilbert space-valued Ornstein-Uhlenbeck process to be reversible with respect to its invariant measure $\mu$. For a reversible process the domain of its generator in $L^p(\mu )$ is…

We study sequences $f_k:\Sigma_k \to \R^n$ of conformally immersed, compact Riemann surfaces with fixed genus and Willmore energy ${\cal W}(f) \leq \Lambda$. Assume that $\Sigma_k$ converges to $\Sigma$ in moduli space, i.e.…

Let $H$ be a compact subgroup of a locally compact group $G$ and let $m$ be the normalized $G$-invariant measure on homogeneous space $G/H$ associated with Weil's formula. Let $\varphi$ be a Young function satisfying $\Delta_2$-condition.…

The fractional integral operators $I_\alpha$ can be used to characterize the Musielak--Orlicz Hardy spaces. This paper shows that for $b\in \rm BMO(\mathbb R^n)$, the commutators $[b,I_\alpha]$ generated by fractional integral operators…

We provide a number of sharp inequalities involving the usual operator norms of Hilbert space operators and powers of the numerical radii. Based on the traditional convexity inequalities for nonnegative real numbers and some generalize…

Let b be a function on the plane. Let H_j, j=1,2, be the Hilbert transform acting on the j-th coordinate on the plane. We show that the operator norm of the double commutator [[ M_b, H_1], H_2] is equivalent to the Chang-Fefferman BMO norm…

In this paper we characterize $m$-isometric and quasi-$m$-isometric weighted conditional type (WCT) operators on the Hilbert space $L^2(\mu)$. Also, we prove that the subclasses of $m$-isometric and quasi-$m$-isometric of normal WCT…

The modular operad $H_\ast(\overline{\mathcal{M}}_{g,n})$ of the homology of Deligne-Mumford compactifications of moduli spaces of pointed Riemann surfaces has a minimal model governed by higher homology operations on the open moduli spaces…

Let $D$ be a pseudoconvex domain in $\C^k_t\times\Cn_z$ and let $\phi$ be a plurisubharmonic function in $D$. For each $t$ we consider the $n$-dimensional slice of $D$, $D_t=\{z; (t,z)\in D\}$, let $\phi^t$ be the restriction of $\phi$ to…

We investigate expansive Hilbert space operators $T$ that are finite rank perturbations of isometric operators. If the spectrum of $T$ is contained in the closed unit disc $\overline{\mathbb{D}}$, then such operators are of the form $T=…

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…

Let $M$ and $N$ be doubly connected Riemann surfaces with $\mathscr{C}^{1,\alpha}$ boundaries and with nonvanishing conformal metrics $\sigma$ and $\wp$ respectively, and assume that $\wp$ is a smooth metric with bounded Gauss curvature…

We give a short proof of the main result of our previous paper [2]: every Schmidt subspace of a Hankel operator is the image of a model space by an isometric multiplier. This class of subspaces is closely related to nearly $S^*$-invariant…

In this paper, we study the Hilbert$-$Schmidt frame (HS-frame) theory for separable Hilbert spaces. We first present some characterizations of HS-frames and prove that HS-frames share many important properties with frames. Then, we show how…

This paper investigates composition operators and weighted composition operators on semi-Hilbert spaces induced by positive multiplication operators on \( L^2(\mu) \). Within the framework of \( A \)-adjoint operators, we characterize…