Related papers: Dynamics of weighted backward shifts on certain an…

The main purpose of this paper is to study the Bishop-Phelps-Bollob\'as property for operators on $c_0$-sum of euclidean spaces. We show that the pair $ (c_0\left(\bigoplus^{\infty}_{k=1}\ell^{k}_{2} \right),Y)$ has the…

Let $(e_i)_i$ denote the unit vector basis of $\ell_p$, $1\leq p< \infty$, or $c_0$. We construct a reflexive Banach space with an unconditional basis that admits $(e_i)_i$ as a uniformly unique spreading model while it has no subspace with…

We show examples of compact linear operators between Banach spaces which cannot be approximated by norm attaining operators. This is the negative answer to an open question posed in the 1970's. Actually, any strictly convex Banach space…

In this paper, we study {\it operator spaces\/} in the sense of the theory developed recently by Blecher-Paulsen [BP] and Effros-Ruan [ER1]. By an operator space, we mean a closed subspace $E\subset B(H)$, with $H$ Hilbert. We will be…

In this paper, we generalize to the context of algebras some recent results on the existence of common hypercyclic vectors for families of products of backward shift operators. We also give, in a multi-dimensional setting, a positive answer…

This paper presents new sequence spaces $X(r, s, t, p ; B)$ for $X \in \{l_\infty(p), c(p), c_0(p), l(p)\}$ defined by using generalized means and difference operator. It is shown that these spaces are complete paranormed spaces and the…

In this paper we consider the reproducing kernel thesis for boundedness and compactness for operators on $\ell^2$--valued Bergman-type spaces. This paper generalizes many well--known results about classical function spaces to their…

We prove that for operators satistying weighted inequalities with $A_p$ weights the boundedness on a certain class of Morrey spaces holds with weights of the form $|x|^\alpha w(x)$ for $w\in A_p$. In the case of power weights the shift with…

For a quasinilpotent operator $T$ on a Banach space $X$, Douglas and Yang defined $k_x=\limsup\limits_{z\rightarrow 0}\frac{\ln\|(z-T)^{-1}x\|}{\ln\|(z-T)^{-1}\|}$ for each nonzero vector $x\in X$, and call $\Lambda(T)=\{k_x: x\ne 0\}$ the…

We consider the shift operator $M_z$, defined on the Bloch space and the little Bloch space and we study the corresponding lattice of invariant subspaces. The index of a closed invariant subspace $E$ is defined as $\text{ind}(E) =…

We consider three problems connected with coinvariant subspaces of the backward shift operator in Hardy spaces $H^p$: 1) properties of truncated Toeplitz operators; 2) Carleson-type embedding theorems for the coinvariant subspaces; 3)…

We study Hardy--Sobolev spaces H_n^p(C^+) on the upper half-plane for 1<=p<=infty and n is a nonnegative integer, from both function-theoretic and operator-theoretic viewpoints. We establish an isometric boundary characterization of…

Let $T$ be a linear operator that, for some $p_1\in(1,\infty)$, is bounded on $L^{p_1}(\tilde w)$ for all $\tilde w\in A_{p_1}(\mathbb R^d)$ and in addition compact on $L^{p_1}(w_1)$ for some $w_1\in A_{p_1}(\mathbb R^d)$. Then $T$ is…

In this paper, we introduce a new class of subsets of bounded linear operators between Banach spaces which is p-version of the uniformly completely continuous sets. Then, we study the relationship between these sets with the equicompact…

In this paper we initiate the study of a fundamental yet untapped random model of non-selfadjoint, bounded linear operators acting on a separable complex Hilbert space. We replace the weights $w_n=1$ in the classical unilateral shift $T$,…

This article is devoted to not only characterizing the first and second preduals of the analytic Campanato spaces ($\mathcal{CA}_p)$ on the unit disk, but also investigating boundedness of three operators: superposition ($\mathsf{S}^\phi$);…

Some new examples of K-monotone couples of the type (X, X(w)), where X is a symmetric space on [0, 1] and w is a weight on [0, 1], are presented. Based on the property of the w-decomposability of a symmetric space we show that, if a weight…

Let $\Omega\subset \mathbb{C}$ be an arbitrary domain in the one-dimensional complex plane equipped with a positive Radon measure $\mu$. For any $1\le p< \infty$, it is shown that the weighted Bergman space $A^p(\Omega, \mu)$ of holomorphic…

We study Birkhoff-James orthogonality of compact (bounded) linear operators between Hilbert spaces and Banach spaces. Applying the notion of semi-inner-products in normed linear spaces and some related geometric ideas, we generalize and…

Let $X^*$ denote a Banach space with a subsymmetric weak$^*$ Schauder basis satisfying condition~\eqref{eq:condition-c}. We show that for any operator $T : X^*\to X^*$, either $T(X^*)$ or $(I-T)(X^*)$ contains a subspace that is isomorphic…