Related papers: Positive operators of Extended Lorentz cones
A criterion and sufficient conditions for a vector to be a cyclic vector for a class of self-adjoint operators are obtained.
A linear operator $T$ between two lattice-normed spaces is said to be $p$-compact if, for any $p$-bounded net $x_\alpha$, the net $Tx_\alpha$ has a $p$-convergent subnet. $p$-Compact operators generalize several known classes of operators…
We consider generalized Hausdorff operators with positive definite and permutable perturbation matrices on Lebesgue spaces and prove that such operators are not Riesz operators provided they are non-zero.
We investigate some types of composition operators, linear and not, and conditions for some spaces to be mapped into themselves and for the operators to satisfy some good properties.
In this paper we consider power means of positive Hilbert space operators both in the conventional and in the Kubo-Ando senses. We describe the corresponding isomorphisms (bijective transformations respecting those means as binary…
Using simultaneously two operator identities, we consider the inversion of the convolution operators on a rectangular. The structure of the inverse operators and of some corresponding forms, which are important in signal processing, is…
This article is a contribution to the spectral theory of so-called eventually positive operators, i.e.\ operators $T$ which may not be positive but whose powers $T^n$ become positive for large enough $n$. While the spectral theory of such…
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.
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 show that a positive operator between $L^p$-spaces is given by integration against a kernel function if and only if the image of each positive function has a lower semi-continuous representative with respect to a suitable topology. This…
It has been very recently discovered that there are compact linear operators between Banach spaces which cannot be approximated by norm attaining operators. The aim of this expository paper is to give an overview of those examples and also…
In this paper, we will address broader concepts for Dunford-Pettis operators, presenting new classes and results that correlate this class with others already well-studied in the literature, as well as an approach outside the origin. We…
We show that for integral operators of general form the norm bounds in Lorentz spaces imply certain norm bounds for the maximal function. As a consequence, the a.e. convergence for the integral operators on the Lorentz spaces follows from…
We establish a spectral characterization theorem for the operators on complex Hilbert spaces of arbitrary dimensions that attain their norm on every closed subspace. The class of these operators is not closed under addition. Nevertheless,…
We give a sufficient condition for a composition operator with positive characteristic to be compact on the Hardy space of Dirichlet series.
In this paper we introduce and study a new sequence of positive linear operators acting on function spaces defined on a convex compact subset. Their construction depends on a given Markov operator, a positive real number and a sequence of…
We study the question when for a given *-algebra $\mathcal{A}$ a sequence of cones $C_n\in M_n(\mathcal{A})$ can be realized as cones of positive operators in a faithful *-representation of $\mathcal{A}$ on a Hilbert space. A…
We investigate the relationship between mapping cones and matrix ordered *-vector spaces (i.e., abstract operator systems). We show that to every mapping cone there is an associated operator system on the space of n-by-n complex matrices,…
We systematically study how properties of abstract operator systems help classifying linear matrix inequality definitions of sets. Our main focus is on polyhedral cones, the 3-dimensional Lorentz cone, where we can completely describe all…
In this paper, we improve the famous Reid Inequality related to linear operators. Some monotony results for positive operators are also established with a different approach from what is known in the existing literature. Lastly, Reid and…