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

In this paper, we compute the exact value of the norm of the Hilbert matrix operator $\mathcal{H}$ acting from the classical Bloch space $\mathcal{B}$ into the logarithmically weighted Bloch space $\mathcal{B}_{\log}$, and show that it…

We compute the exact value of the essential norm of a generalized Hilbert matrix operator acting on weighted Bergman spaces $A^p_v$ and weighted Banach spaces $H^\infty_v$ of analytic functions, where $v$ is a general radial weight. In…

In this paper, we determine the exact norm of the Ces\`aro operator $\mathcal{C}$ on the Korenblum space $H^\infty_\alpha$ for $0 < \alpha \leq \frac12$ and on the logarithmically weighted space $H^\infty_{\alpha,\log}$ for $0 < \alpha <…

Very recently, Bo\v{z}in and Karapetrovi\'c solved a conjecture by proving that the norm of the Hilbert matrix operator $\mathcal{H}$ on the Bergman space $A^p$ is equal to $\frac{\pi}{\sin(\frac{2\pi}{p})}$ for $2 < p < 4.$ In this article…

In this article we study the action of the the Hilbert matrix operator $\mathcal H$ from the space of bounded analytic functions into conformally invariant Banach spaces. In particular, we describe the norm of $\mathcal{H}$ from $H^\infty$…

It is well known that the Hilbert matrix operator $\mathcal {H}$ is bounded from $H^{\infty}$ to the mean Lipschitz spaces $\Lambda^{p}_{\frac{1}{p}}$ for all $1<p<\infty$. In this paper, we prove that the range of Hilbert matrix operator…

In this article, the open problem of finding the exact value of the norm of the Hilbert matrix operator on weighted Bergman spaces $A^p_\alpha$ is adressed. The norm was conjectured to be $\frac{\pi}{\sin \frac{(2+\alpha)\pi}{p}}$ by…

This paper is a continuation of a recent work on a new norm, christened the $ (\alpha, \beta)$-norm, on the space of bounded linear operators on a Hilbert space. We obtain some upper bounds for the said norm of $n\times n$ operator…

Let $\Omega_+$ be either the open unit disc or the open upper half plane or the open right half plane. In this paper, we compute the norm of the basic operator $A_\alpha=\Pi_\Theta T_{b_\alpha}|_{\mathcal{H}(\Theta)}$ in the vector valued…

Karapetrovi\'c conjectured that the norm of the Hilbert matrix operator on the Bergman space $A^p_\alpha$ is equal to $\pi/\sin((2+\alpha)\pi/p)$ when $-1<\alpha<p-2$. In this paper, we provide a proof of this conjecture for $0\leq \alpha…

Let $\mu$ be a positive Borel measure on the interval $[0,1)$. The Hankel matrix $\mathcal{H}_\mu=(\mu_{n+k})_{n,k\geq 0}$ with entries $\mu_{n,k}=\mu_{n+k}$ induces the operator $$…

The value of the operator norm of Bergman projections from $L^{\infty}(\mathbb{B}^n)$ to Bloch space is found in \cite{KalajMarkovic2014}. The authors of mentioned paper proposed the problem of calculating the norm of the same class of…

Let $\alpha>0$ and $\mu$ be a positive Borel measure on the interval $[0,1)$. The Hankel matrix $\mathcal{H}_{\mu,\alpha}=(\mu_{n,k,\alpha})_{n,k\ge0}$ with entries…

Let ${\mathbb B}(\mathscr H)$ denote the set of all bounded linear operators on a complex Hilbert space ${\mathscr H}$. In this paper, we present some norm inequalities for sums of operators which are a generalization of some recent…

The Hilbert matrix $\mathcal{H}_{n,m} = (n+m+ 1)^{-1}$ has been extensively studied in previous literature. In this paper we look at generalized Hilbert operators arising from measures on the interval $[0, 1]$, such that the Hilbert matrix…

Let $H(\mathbb{D})$ be the space of all analytic functions in the unit disc $\mathbb{D}$. For $g\in H(\mathbb{D})$, the generalized Hilbert operator $\mathcal{H}_{g}$ is defined by $$\mathcal{H}_{g}(f)(z)=\int_{0}^{1}f(t)g'(tz)dt, \ \ z\in…

Let $f$ be a symmetric norm on ${\mathbb R}^n$ and let ${\mathcal B}({\mathcal H})$ be the set of all bounded linear operators on a Hilbert space ${\mathcal H}$ of dimension at least $n$. Define a norm on ${\mathcal B}({\mathcal H})$ by…

Let $H$ be a reflexive, dense, separable, infinite dimensional complex Hilbert space and let $B(H)$ be the algebra of all bounded linear operators on $H$. In this paper, we carry out characterizations of norm-attainable operators in normed…

Let $\mu$ be a positive Borel measure on the interval [0,1). For $\alpha>0$, the Hankel matrix $\mathcal{H}_{\mu,\alpha}=(\mu_{n,k,\alpha})_{n,k\geq 0}$ with entries…

An operator $T$ acting on a Hilbert space is called $(\alpha ,\beta)$-normal ($0\leq \alpha \leq 1\leq \beta $) if \begin{equation*} \alpha ^{2}T^{\ast }T\leq TT^{\ast}\leq \beta ^{2}T^{\ast}T. \end{equation*} In this paper we establish…