Related papers: Generalized Hilbert matrix operators acting on Ber…

We study the boundedness of the linear operator $S$ on $L^{p}_{a}(dA_{\alpha})$ $(0<p<\infty)$. In particular, we obtain a sufficient and necessary condition for the compactness of the linear operator $S$ on $L^{p}_{a}(dA_{\alpha})$…

We characterize those bounded multilinear operators that factor through a Hilbert space in terms of its behavior in finite sequences. This extends a result, essentially due to S. Kwapie\'{n}, from the linear to the multilinear setting. We…

Let $\mu$ be a positive Borel measure on the interval $[0,1)$. The Hankel matrix $\mathcal{H}_{\mu}=(\mu_{n,k})_{n,k\geq0}$ with entries $\mu_{n,k}=\mu_{n+k}$, where $\mu_n=\int_{[0,1)}t^{n}d\mu(t)$. For $f(z)=\sum_{n=0}^{\infty}a_nz^n$ is…

In this paper, we consider composition operators on weighted Hilbert spaces of analytic functions and observe that a formula for the essential norm, give a Hilbert-Schmidt characterization and characterize the membership in Schatten-class…

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…

Given a positive Borel measure $\mu$ on $[0,1)$ and a parameter $\beta>0$, we consider the Ces\`aro-type operator $\mathcal C_{\mu,\beta}$ acting on the analytic function $f(z)=\sum_{n=0}^\infty a_n z^n$ on the unit disc of the complex…

We study generalized polar decompositions of densely defined, closed linear operators in Hilbert spaces and provide some applications to relatively (form) bounded and relatively (form) compact perturbations of self-adjoint, normal, and…

We obtain upper bounds for the numerical radius of a product of Hilbert space operators which improve on the existing upper bounds. We generalize the numerical radius inequalities of $n\times n$ operator matrices by using non-negative…

Several unitarily invariant norm inequalities and numerical radius inequalities for Hilbert space operators are studied. We investigate some necessary and sufficient conditions for the parallelism of two bounded operators. For a finite rank…

In this paper, we generalize the notion of joint eigenvalues and joint spectrum of matrices and operator tupples on a bi complex Hilbert space. We observe that unlike the spectrum of a bounded operator on a bi complex Hilbert space is…

For $-1<\alpha<\infty$, let $\omega_\alpha(z)=(1+\alpha)(1-|z|^2)^\alpha$ be the standard weight on the unit disk. In this note, we provide descriptions of the boundedness and compactness for the Toeplitz operators $T_{\mu,\beta}$ between…

Let $A$ be a Banach space, $p>1$, and $1/p+1/q=1$. If a sequence $a=(a_i)$ in $A$ has a finite $p$-sum, then the operator $\Lambda_a:\ell^q\to A$, defined by $\Lambda_a(\beta)=\sum_{i=1}^\infty \beta_i a_i, \beta=(\beta_i)\in \ell^q$, is…

An investigation is made of the generalized Ces\`aro operators $C_t$, for $t\in [0,1]$, when they act on the space $H(\mathbb{D})$ of holomorphic functions on the open unit disc $\mathbb{D}$, on the Banach space $H^\infty$ of bounded…

The finite entropy of black holes suggests that local regions of spacetime are described by finite-dimensional factors of Hilbert space, in contrast with the infinite-dimensional Hilbert spaces of quantum field theory. With this in mind, we…

We introduce a notion of joint spectrum for a tuple of compact operators on a separable Hilbert space and show that in many situations these operators commute if and only if the joint spectrum consists of countably many, locally finite,…

In this paper we define a space $\ghu{M}$ of Hardy--Goldberg type on a measured metric space satisfying some mild conditions. We prove that the dual of $\ghu{M}$ may be identified with $\gbmo{M}$, a space of functions with "local" bounded…

It is shown that the algebra \(L^\infty(\mu)\) of all bounded measurable functions with respect to a finite measure \(\mu\) is localizing on the Hilbert space \(L^2(\mu)\) if and only if the measure \(\mu\) has an atom. Next, it is shown…

We reconsider studies of Toeplitz operators on function spaces (the weighted Bergman space, the generalized derivative Hardy space) and the H-Toeplitz operators on the Bergman space. Past studies have considered the presence or absence of…

Let $\mathcal{H}$ be a complex Hilbert space and let $A$ be a positive operator on $\mathcal{H}$. We obtain new bounds for the $A$-numerical radius of operators in semi-Hilbertian space $\mathcal{B}_A(\mathcal{H})$ that generalize and…

We consider the Hilbert-type operator defined by $$ H_{\omega}(f)(z)=\int_0^1 f(t)\left(\frac{1}{z}\int_0^z B^{\omega}_t(u)\,du\right)\,\omega(t)dt,$$ where $\{B^{\omega}_\zeta\}_{\zeta\in\mathbb{D}}$ are the reproducing kernels of the…