Related papers: Trace-Class and Nuclear Operators
This paper generalizes results for alternate dual frames in Hilbert spaces on the situation of a Banach space. Additionally some properties of synthesys operator associated with alternate dual frame are investigated. The main result is that…
Let $A$ and $B$ be two densely defined unbounded closeable operators in a Hilbert space such that their unbounded operator products $AB$ and $BA$ are also densely defined. Then all four operators possess adjoints and we obtain new inclusion…
We introduce the main concepts and announce the main results in a theory of tensor products for module categories for a vertex operator algebra. This theory is being developed in a series of papers including hep-th 9309076 and hep-th…
In this article, concepts of well- and ill-posedness for linear operators in Hilbert and Banach spaces are discussed. While these concepts are well understood in Hilbert spaces, this is not the case in Banach spaces, as there are several…
We study operators acting on a tensor product Hilbert space and investigate their product numerical range, product numerical radius and separable numerical range. Concrete bounds for the product numerical range for Hermitian operators are…
Given a set $B$ of operators between subspaces of $L_p$ spaces, we characterize the operators between subspaces of $L_p$ spaces that remain bounded on the $X$-valued $L_p$ space for every Banach space on which elements of the original class…
We consider real spaces only. Definition. An operator $T:X\to Y$ between Banach spaces $X$ and $Y$ is called a Hahn-Banach operator if for every isometric embedding of the space $X$ into a Banach space $Z$ there exists a norm-preserving…
A bounded linear operator $T$ on a Banach space $X$ is called hypercyclic if there exists a vector $x \in X$ such that $orb{(x,T)}$ is dense in $X$. The Hypercyclicity Criterion is a well-known sufficient condition for an operator to be…
In past few decades, tensor algebra also known as multi-linear algebra has been developed and customized as a tool to be used for various engineering applications. In particular, with the help of a special form of tensor contracted product,…
We introduce a construction that turns a category of pure state spaces and operators into a category of observable algebras and superoperators. For example, it turns the category of finite-dimensional Hilbert spaces into the category of…
We present other examples illustrating the operator-theoretic approach to invariant integrals on quantum homogeneous spaces developed by Kuersten and the second author. The quantum spaces are chosen such that their coordinate algebras do…
The concept of complementability is extended from bounded operators to densely defined operators on Hilbert spaces. By introducing appropriate projections and decomposition techniques, a framework is developed for analyzing…
In this paper, we investigate whether the tensor product of two frames, each individually localised with respect to a spectral matrix algebra, is also localised with respect to a suitably chosen tensor product algebra. We provide a partial…
In the framework of quantum mechanics over a quadratic extension of the ultrametric field of p-adic numbers, we introduce a notion of tensor product of p-adic Hilbert spaces. To this end, following a standard approach, we first consider the…
A proto-quantum space is a (general) matricially normed space in the sense of Effros and Ruan presented in a `matrix-free' language. We show that these spaces have a special (projective) tensor product possessing the universal property with…
Notion of frames and Bessel sequences for metric spaces have been introduced. This notion is related with the notion of Lipschitz free Banach spaces. \ It is proved that every separable metric space admits a metric $\mathcal{M}_d$-frame.…
This paper is concerned with paired operators in the context of the Lebesgue Hilbert space on the unit circle and its subspace, the Hardy space. By considering when such operators commute, generalizations of the Brown--Halmos results for…
We study unital operator spaces endowed with a partially defined product. We give a matrix-norm characterization of such products that allows for a representation theorem where the partial product is realized as composition of operators on…
Given a braided pivotal category $\mathcal C$ and a pivotal module tensor category $\mathcal M$, we define a functor $\mathrm{Tr}_{\mathcal C}:\mathcal M \to \mathcal C$, called the associated categorified trace. By a result of…
The aim of this paper is to extend the notion of Apq space from its historical context in the work of Herz and to recognise such spaces as preduals of spaces of intertwining operators of induced representations as suggested by the work of…