Related papers: An example of weakly amenable and character amenab…

In this paper we define $\lambda$-hyponormal operators on an infinite dimensional Hilbert space $\mathcal{H}$ and find a class of $\lambda$-hyponormal operators that can not be hypercyclic. Also, we study closedness of range and…

In the present article we review an approximation procedure for amenable traces on unital and separable C*-algebras acting on a Hilbert space in terms of F\o lner sequences of non-zero finite rank projections. We apply this method to…

A set of bounded linear operators from a Banach space to a Banach lattice is collectively L-weakly compact whenever union of images of the unit ball is L-weakly compact. We extend the Meyer-Nieberg duality theorem to collectively L-weakly…

Let $T$ be a $C_0$--contraction on a separable Hilbert space. We assume that $I_H-T^*T$ is compact. For a function $f$ holomorphic in the unit disk $\DD$ and continuous on $\bar\DD$, we show that $f(T)$ is compact if and only if $f$…

For $0<p\leq\infty$, let $F^{p}_\varphi$ be the Fock space induced by a weight function $\varphi$ satisfying $ dd^c \varphi \simeq \omega_0$. In this paper, given $p\in (0, 1]$ we introduce the concept of weakly localized operators on $…

In this paper we use orthonormal basis for the Hardy space $H^{2}(\mathbb{T})$, formed by rational functions, to characterize complex symmetric Toeplitz operators on $H^{2}(\mathbb{T})$. As a result, we get examples of these operators whose…

This paper considers paired operators in the context of the Lebesgue Hilbert space $L^2$ on the unit circle and its subspace, the Hardy space $H^2$. The kernels of such operators, together with their analytic projections, which are…

We introduce a notion of tractability for ill-posed operator equations in Hilbert space. For such operator equations the asymptotics of the best possible rate of reconstruction in terms of the underlying noise level is known in many cases.…

In the present work we characterized full operators and we showed some properties that have nonfull injectives operators. With the results developed for full operators, we affirmatively respond two questions formulated by Bravo and Feintuch…

We present the weighted weak group inverse, which is a new generalized inverse of operators between two Hilbert spaces, introduced to extend weak group inverse for square matrices. Some characterizations and representations of the weighted…

If $T$ is a polynomially bounded operator, $\mathcal M$ is an invariant subspace of $T$, $T|_{\mathcal M}$ is a unilateral shift and $T^*|_{\mathcal M^\perp}$ is subnormal, then $T$ has a nontrivial hyperinvariant subspace. If an operator…

Let $\mathcal H$ and $\mathcal K$ be real Hilbert spaces and $T \in \mathcal{B} (\mathcal H,\mathcal K)$ an injective operator with closed range and Moore-Penrose inverse $T^\dagger$. Based on the well-known characterization of proximity…

In this paper, we introduce and study the class of {\it enriched strictly pseudocontractive mappings} in Hilbert spaces and extend the corresponding convergence theorem (Theorem 12) in [Browder, F. E., Petryshyn, W. V., {\it Construction of…

The classical theory of Toeplitz operators in spaces of analytic functions deals usually with symbols that are bounded measurable functions on the domain in question. A further extension of the theory was made for symbols being unbounded…

In this article, we briefly describe nearly $T^{-1}$ invariant subspaces with finite defect for a shift operator $T$ having finite multiplicity acting on a separable Hilbert space $\mathcal{H}$ as a generalization of nearly $T^{-1}$…

We consider tractability of integration in reproducing kernel Hilbert spaces which are a tensor product of a Walsh space and a Korobov space. The main result provides necessary and sufficient conditions for weak, polynomial and strong…

Let $\mathcal G$ be a Hilbert space and $\mathfrak B(\mathcal G)$ the algebra of bounded operators, $\mathcal H=L_2([0,\infty);\mathcal G)$. An operator-valued function $Q\in L_{\infty,\rm loc}\left([0,\infty);\mathfrak B(\mathcal…

We continue our analysis of the consequences of the commutation relation $[S,T]=\Id$, where $S$ and $T$ are two closable unbounded operators. The {\em weak} sense of this commutator is given in terms of the inner product of the Hilbert…

We show that finitely subgraded Lie algebras of compact operators have invariant subspaces when conditions of quasinilpotence are imposed on certain components of the subgrading. This allows us to obtain some useful information about the…

We introduce the class of unbounded $M$-weakly operators and the class of unbounded $L$-weakly compact operators. We investigate some properties for these new classification of operators and we study relation between them and $M$-weakly…