Related papers: Positive Hankel operators, positive definite kerne…

In the context of kernel optimization, we prove a result that yields new factorizations and realizations. Our initial context is that of general positive operator-valued kernels. We further present implications for Hilbert space-valued…

Given Hilbert space operators $P,T\in B(\H), P\geq 0$ invertible, $T$ is $(m,P)-$ expansive (resp., $(m,P)-$ isometric) for some positive integer $m$ if…

We show, by means of a class of examples, that if $K_1$ and $K_2$ are two positive definite kernels on the unit disc such that the multiplication by the coordinate function on the corresponding reproducing kernel Hilbert space is subnormal,…

We introduce a vector differential operator $\mathbf{P}$ and a vector boundary operator $\mathbf{B}$ to derive a reproducing kernel along with its associated Hilbert space which is shown to be embedded in a classical Sobolev space. This…

We generalize a preceding simple proof of the Jamiolkowski criterion to check whether a given linear map between algebras of operators is completely positive or not. The generalization is performed to embrace all algebras of Hilbert-Schmidt…

We define an extension of operator-valued positive definite functions from the real or complex setting to topological algebras, and describe their associated reproducing kernel spaces. The case of entire functions is of special interest,…

In this paper, we describe families of those bounded linear operators on a separable Hilbert space that are simultaneously unitarily equivalent to integral operators on $L_2(R)$ with bounded and arbitrarily smooth Carleman kernels. The main…

A complete characterization of Hilbert space operators that generate weakly amenable algebras remains open, even in the case of compact operator. Farenick, Forrest and Marcoux proposed the question that if $T$ is a compact weakly amenable…

Let $(X,\mu)$ be a strictly-positive Borel measure space. We show that the modes of convergence in a reproducing kernel Hilbert (RKHS) space, pointwise, weak and strong are all equivalents. From this we describe some important consequences…

Let $\mathcal{H}$ be a separable Hilbert space and let $A^{2}_{\varphi}(\mathcal{H})$ be the $\mathcal{H}$-valued Bergman spaces with exponential weights. In the present paper, we give the complete characterizations for the boundedness and…

We consider an inverse spectral problem for a class of non-compact Hankel operators $H$ such that the modulus of $H$ (restricted onto the orthogonal complement to its kernel) has simple spectrum. Similarly to the case of compact operators,…

Given a reproducing kernel Hilbert space H of real-valued functions and a suitable measure mu over the source space D (subset of R), we decompose H as the sum of a subspace of centered functions for mu and its orthogonal in H. This…

We define essentially positive operators on Hilbert space as a class of self-adjoint operators whose essential spectra is contained in the nonnegative real numbers and describe their basic properties. Using Toeplitz operators and the…

In this paper we study positive fixed points of Hammerstein integral operators with degenerate kernel in the cone of C[0, 1]. Problem on a number of positive fixed points of the Hammerstein integral operator leads to the study positive…

In this paper, we aim to introduce and characterize the concept of numerical radius orthogonality of operators on a complex Hilbert space $\mathcal{H}$ which are bounded with respect to the semi-norm induced by a positive operator $A$ on…

In this paper we show how specific families of positive definite kernels serve as powerful tools in analyses of iteration algorithms for multiple layer feedforward Neural Network models. Our focus is on particular kernels that adapt well to…

In topological equivalence, a bounded linear operator between Banach spaces - we focus on the case of Hilbert spaces - is viewed as only acting linearly and continuously between them qua different spaces with the structure of linear…

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 demonstrate new abstract characterizations for unital and non-unital operator spaces. We characterize unital operator spaces in terms of the cone of accretive operators (operators whose real part is positive). Defining the gauge of an…

The positive definiteness of real quadratic forms with convolution structures plays an important role in stability analysis for time-stepping schemes for nonlocal operators.In this work, we present a novel analysis tool to handle discrete…