Related papers: J-fusion frame operator for Krein spaces

In this paper we obtain necessary and sufficient conditions for a linear bounded operator in a Hilbert space $H$ to have a three-diagonal complex symmetric matrix with non-zero elements on the first sub-diagonal in an orthonormal basis in…

In this article a class of closed convex sets in the Euclidean $n$-space which are the convex hull of their profiles is described. Thus a generalization of Krein-Milman theorem\cite{Lay:1982} to a class of closed non-compact convex sets is…

The concept of operator frame can be considered as a generalization of frame. Firstly, we introduce the notion of operator frame for the set of all adjointable operators $Hom_{\mathcal{A}}^{\ast}(\mathcal{X})$ on a Hilbert…

Ambiguities arising in different approaches (canonical, quasiclassical, path integration) to quantization are discussed by an example of the mechanics of a point-like particle in the Riemannian space (the geodesic dynamics). A way to select…

We consider the decomposition of bounded linear operators on Hilbert spaces in terms of functions forming frames. Similar to the singular-value decomposition, the resulting frame decompositions encode information on the structure and…

In the paper, we investigate weighted composition operators on Bergman spaces of a half-plane. We characterize weighted composition operators which are hermitian and those which are complex symmetric with respect to a family of…

The possibility of defining sesquilinear forms starting from one or two sequences of elements of a Hilbert space is investigated. One can associate operators to these forms and in particular look for conditions to apply representation…

We construct embeddings of boundary algebras B into ZF algebras A. Since it is known that these algebras are the relevant ones for the study of quantum integrable systems (with boundaries for B and without for A), this connection allows to…

In this paper, we study a class of multilinear fractional integral operators which have correlation kernels $\prod_{1\leq i<j \leq k}|x_i-x_j|^{-\alpha_{ij}}$. The necessary and sufficient conditions are obtained under which these oprators…

In this paper we first introduce the extended limit set $J_{\{T^n\}}(x)$ for a sequence of bounded linear operators $\{T_n\}_{n=1}^{\infty}$ on a separable Banach space $X$ . Then we study the dynamics of sequence of linear operators by…

A special class of generalized Jacobi operators which are self-adjoint in Krein spaces is presented. A description of the resolvent set of such operators in terms of solutions of the corresponding recurrence relations is given. In…

The paper is concerned with the following question: if $A$ and $B$ are two bounded operators between Hilbert spaces $\mathcal{H}$ and $\mathcal{K}$, and $\mathcal{M}$ and $\mathcal{N}$ are two closed subspaces in $\mathcal{H}$, when will…

In this paper, we study the weighted composition operator on the Fock space $\mf$ of slice regular functions. First, we characterize the boundedness and compactness of the weighted composition operator. Subsequently, we describe all the…

We study the minimizers of the fusion frame potential in the case that both the weights and the dimensions of the subspaces are fixed and not necessarily equal. Using a concept of irregularity we provide a description of the local (that are…

Krein space quantization and the ambient space formalism have been successfully applied to address challenges in quantum geometry (e.g., quantum gravity) and the axiomatic formulation of quantum Yang-Mills theory, including phenomena such…

The main result of this paper is a description of the space of functions on the unit circle, for which Krein's trace formula holds for arbitrary pairs of unitary operators with trace class difference. This space coincides with the space of…

In [22], the authors proved a Kastler-Kalau-Walze type theorem for the J-twist D_J of the Dirac operator on 3-dimensional and 4-dimensional almost product Riemannian spin manifold with boundary. In this paper, we develop the…

In the present paper the unconditional convergence and the invertibility of multipliers is investigated. Multipliers are operators created by (frame-like) analysis, multiplication by a fixed symbol, and resynthesis. Sufficient and/or…

If $T$ is a semibounded self-adjoint operator in a Hilbert space $(H, \, (\cdot , \cdot))$ then the closure of the sesquilinear form $(T \cdot , \cdot)$ is a unique Hilbert space completion. In the non-semibounded case a closure is a…

It is well known that the unboundedness of operators in Hilbert space entails domain troubles. It is also well known that most domain troubles can be surmounted by extending the Hilbert space to a rigged Hilbert space. In this note, we…