Related papers: Conditions of fixed sign for $n\times n$ operator …
Let $A_{1}$, $A_{2}$, $...$, $A_{k}$ be strictly positive operators on a Hilbert space. This note is to show a sufficient condition of $A_{k}\geq A_{k-1}\geq\geq A_{3}\geq A_{2}\geq A_{1}$, which extends the related result before.
We give necessary and sufficient conditions for an operator on a separable Hilbert space to satisfy the hypercyclicity criterion.
In general, it is a non trivial task to determine the adjoint $S^*$ of an unbounded operator $S$ acting between two Hilbert spaces. We provide necessary and sufficient conditions for a given operator $T$ to be identical with $S^*$. In our…
We study approximations of compact linear multivariate operators defined over Hilbert spaces. We provide necessary and sufficient conditions on various notions of tractability. These conditions are mainly given in terms of sums of certain…
Some new characterizations of nonnegative Hamiltonian operator matrices are given. Several necessary and sufficient conditions for an unbounded nonnegative Hamiltonian operators to be invertible are obtained; so that the main results in the…
Operator matrices have played a significant role in studying Hilbert space operators. In this paper, we discuss further properties of operator matrices and present new estimates for the operator norms and numerical radii of such operators.…
We propose two interrelated advances in the theory of adjointable operators on Hilbert C*-modules. First, we give a set of equivalent, verifiable conditions characterizing positivity of general $n\times n$ block operator matrices acting on…
This paper investigates spectral properties of certain classes of positive operators originated from different matrices appeared in linear complementarity problem. These positive operators play a crucial role in various areas of mathematics…
It is shown that a positive (bounded linear) operator on a Hilbert space with trivial kernel is unitarily equivalent to a Hankel operator that satisfies double positivity condition if and only if it is non-invertible and has simple spectrum…
We provide sufficient and necessary conditions guaranteeing equations $(A+B)^*=A^*+B^*$ and $(AB)^*=B^*A^*$ concerning densely defined unbounded operators $A,B$ between Hilbert spaces. We also improve the perturbation theory of selfadjoint…
We give necessary and sufficient conditions for a bounded operator defined between complex Hilbert spaces to be absolutely norm attaining. We discuss structure of such operators in the case of self-adjoint and normal operators separately.…
To a generalized tight continuous frame in a Hilbert space $\H$ indexed by a locally compact space $\Si$ endowed with a Radon measure, one associates a coorbit theory converting spaces of functions on $\Si$ in spaces of vectors comparable…
We study basic spectral properties of J-self-adjoint $2\times 2$ block operator matrices. Using the linear resolvent growth condition, we obtain simple necessary conditions for the regularity of the critical point $\infty$. In particular,…
A criterion and sufficient conditions for a vector to be a cyclic vector for a class of self-adjoint operators are obtained.
This paper presents necessary and sufficient conditions for a positive bounded operator on a separable Hilbert space to be the sum of a finite or infinite collection of projections (not necessarily mutually orthogonal), with the sum…
We present an inequality for tensor product of positive operators on Hilbert spaces by considering the tensor product of operators as words on certain alphabets (i.e., a set of letters). As applications of the operator inequality and by a…
We obtain upper bounds for the numerical radius of a product of Hilbert space operators which improve on the existing upper bounds. We generalize the numerical radius inequalities of $n\times n$ operator matrices by using non-negative…
In this paper we provide a criterion of essential self-adjointness for operators in the tensor product of a separable Hilbert space and a Fock space. The class of operators we consider may contain a self-adjoint part, a part that preserves…
The main purpose of this paper is, in the general setting of the adjointable operators on Hilbert $C^*$-modules, to develop two new tools that can be applied to deal with the positive solutions of certain operator equations, the operator…
Important features of certain economic models may be revealed by studying positive eigenfunctions of appropriately chosen linear operators. Examples include long-run risk-return relationships in dynamic asset pricing models and components…