相关论文: Some necessary and sufficient conditions for Hyper…

We study hypercyclicity of the Toeplitz operators in the Hardy space $H^2(\mathbb{D})$ with symbols of the form $p(\bar{z}) +\phi(z)$, where $p$ is a polynomial and $\phi \in H^\infty(\mathbb{D})$. We find both necessary and sufficient…

The basic purpose of the present paper is the full solutions of the inverse problem (i.e. a finding of necessary and sufficient conditions) for the operator with complex periodic coefficients.

We present three necessary separability criteria for bipartite mixed states, the violation of each of these conditions is a sufficient condition for entanglement. Some ideas on the issue of finding a necessary and sufficient criterion of…

In this paper we establish hypercyclicity of continuous linear operators on $H(\mathbb{C})$ that satisfy certain commutation relations.

In this paper, we show that if the direct sum of two operators is subspace-hypercyclic (satisfies subspace hypercyclic criterion), then both operators are subspace-hypercyclic (satisfy subspace hypercyclic criterion). Moreover, if an…

A bounded linear operator $T$ on a Banach space $X$ is called subspace-hypercyclic if there is a subspace $M \subsetneq X$ and a vector $x \in X$ such that $orb{(x,T)} \cap M$ is dense in $M$. We show that every Banach space supports…

A new hierarchy of separability conditions for bipartite states is obtained. All the conditions in the hierarchy are necessary for separability. The conditions are expressed in terms of higher powers of the density operator of the bipartite…

In this paper we characterize mixing composition operators acting on the space $\mathscr{O}_M(\mathbb{R})$ of slowly increasing smooth functions. Moreover we relate the mixing property of those operators with the solvability of Abel's…

Necessary and sufficient conditions for the existence of a composite-system statistical operator, and, separately, for the possibility of its being correlated or uncorrelated, are derived in terms of its range dimension and the range…

Proper splittings of operators are commonly used to study the convergence of iterative processes. In order to approximate solutions of operator equations, in this article we deal with proper splittings of closed range bounded linear…

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.…

We provide conditions for a linear map of the form $C_{R,T}(S)=RST$ to be $q$-frequently hypercyclic on algebras of operators on separable Banach spaces. In particular, if $R$ is a bounded operator satisfying the $q$-Frequent Hypercyclicity…

In this article we study different aspects of Hermitian operators applying the concept of positive decompositions. On the one hand, we characterize the positivity of an Hermitian operator by means of a norm condition where the factors of…

In this note, we provide some sufficient and necessary conditions for the core inverse of the perturbed operator to have the simplest possible expression. The results improve the recent work by H. Ma (Optimal perturbation bounds for the…

We establish necessary and sufficient conditions for boundedness of composition operators on the most general class of Hilbert spaces of entire Dirichlet series with real frequencies. Depending on whether or not the space contains any…

We demonstrate that being a hyperbolicity preserver does not imply monotonicity for infinite order differential operators on $\mathbb{R}[x]$, thereby settling a recent conjecture in the negative. We also give some sufficient conditions for…

We first generalize the results of Le\'on and M\"uller [Studia Math. 175(1) 2006] on hypercyclic subspaces to sequences of operators on Fr\'echet spaces with a continuous norm. Then we study the particular case of iterates of an operator T…

A bounded operator on a real or complex separable infinite-dimensional Banach space $Z$ is universal in the sense of Glasner and Weiss if for every invertible ergodic measure-preserving transformation $T$ of a standard Lebesgue probability…

In this work, an operator superquadratic function (in operator sense) for positive Hilbert space operators is defined. Several examples with some important properties together with some observations which are related to the operator…

Even linear operators on infinite-dimensional spaces can display interesting dynamical properties and yield important links among functional analysis, differential and global geometry and dynamical systems, with a wide range of…