相关论文: Norm of the Hilbert matrix operator between some s…

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 complex numbers $a, b, c$ and a non-negative continuous function $\varphi$ defined on $[0, +\infty)$, consider the $2 \times 2$ matrix $$ M_t = \begin{pmatrix} a & t \\ ct & b\varphi(t) \end{pmatrix}, \quad t \in [0, +\infty). $$ We…

We consider operators acting on a Hilbert space that can be written as the sum of a shift and a diagonal operator and determine when the operator is hyponormal. The condition is presented in terms of the norm of an explicit block Jacobi…

We introduce a new norm on the space of bounded linear operators on a complex Hilbert space, which generalizes the numerical radius norm, the usual operator norm and the modified Davis-Wielandt radius. We study basic properties of this…

In this note, we introduce a novel norm, termed the $t-$Berezin norm, on the algebra of all bounded linear operators defined on a reproducing kernel Hilbert space $\mathcal{H}$ as $$\|A\|_{t-ber} = \sup_{ \lambda, \mu \in \Omega} \left\{…

If $\mu $ is a positive Borel measure on the interval $[0, 1)$ we let $\mathcal H_\mu $ be the Hankel matrix $\mathcal H_\mu =(\mu_{n, k})_{n,k\ge 0}$ with entries $\mu_{n, k}=\mu_{n+k}$, where, for $n\,=\,0, 1, 2, \dots $, $\mu_n$ denotes…

Let $\mathscr{H}$ be a complex Hilbert space, and let $\mathscr{B}(\mathscr{H})$ denote the set of all bounded operators on $\mathscr{H}$ . For an operator $T \in \mathscr{B}(\mathscr{H})$, let $|T| := (T^*T)^{\frac{1}{2}}$. For $A$ in…

We introduce the notions of L(H)-valued norms and Banach spaces with respect to L(H)-valued norms. In particular, we introduce Hilbert spaces with respect to L(H)-valued inner products. In addition, we provide several fundamental examples…

In this paper we introduce and study some Hilbert-type operators acting from the function spaces into the sequence spaces. We give some sufficient and necessary conditions for the boundedness and compactness of these Hilbert-type operators.…

If $\mu $ is a positive Borel measure on the interval $[0, 1)$ we let $\mathcal H_\mu $ be the Hankel matrix $\mathcal H_\mu =(\mu _{n, k})_{n,k\ge 0}$ with entries $\mu _{n, k}=\mu _{n+k}$, where, for $n\,=\,0, 1, 2, \dots $, $\mu_n$…

We consider weighted Bergman projection $P_{\alpha}: L^{\infty}(\Bbb B) \rightarrow {\cal B} $ where $\alpha>-1$ and $\cal B$ is the Bloch space of the unit ball $\Bbb B$ of the complex space $\Bbb C^n.$ We obtain the exact norm of the…

The paper is devoted to the problem of exact calculation of the norms in ideal spaces for monotone operators on the cones of functions with monotonicity properties. We implement a general approach to this problem that covers many concrete…

In this article we study the generalized Hilbert matrix operator $\Gamma_\mu$ acting on the Bergman spaces $A^p$ of the unit disc for $1\leq p<\infty$. In particular, we characterize the measures $\mu$ for which the operator $\Gamma_\mu$ is…

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 will consider matrices with entries in the space of operators $\mathcal{B}(H)$, where $H$ is a separable Hilbert space and consider the class of matrices that can be approached in the operator norm by matrices with a…

Let $H$ be a Hilbert space that can be embedded as a dense subspace of a Banach space $X$ such that the norm of the embedding is equal to $1$. We consider the following statements for a nonzero vector $\varphi$ in $H$: (A) $\|\varphi\|_X =…

Let $X$ be a Banach function space over the unit circle such that the Riesz projection $P$ is bounded on $X$ and let $H[X]$ be the abstract Hardy space built upon $X$. We show that the essential norm of the Toeplitz operator $T(a):H[X]\to…

Let $A$ be a positive definite operator on a Hilbert space $H$, and $|||.|||$ be a unitarily invariant norm on $B(H)$. We show that if $f$ is an operator monotone function on $(0,\infty)$ and $n\in \mathbb{N}$, then $|||D^n…

Let ($\mathcal{H}, \langle . , .\rangle )$ be a complex Hilbert space and $A$ be a positive bounded linear operator on it. Let $w_A(T)$ be the $A$-numerical radius and $\|T\|_A$ be the $A$-operator seminorm of an operator $T$ acting on the…

If $\,\mu \,$ is a finite positive Borel measure on the interval $\,[0,1)$, we let $\,\mathcal H_\mu \,$ be the Hankel matrix $\,(\mu _{n, k})_{n,k\ge 0}\,$ with entries $\,\mu _{n, k}=\mu _{n+k}$, where, for $\,n\,=\,0, 1, 2, \dots $,…