Related papers: Partial Inner Products on Antiduals

Some reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in complex Hilbert spaces are given. Applications for complex-valued functions are provided as well.

A Hilbert module is a generalisation of a Hilbert space for which the inner product takes its values in a C*-algebra instead of the complex numbers. We use the bracket product to construct some Hilbert modules over a group C*-algebra which…

The aim of this paper is to investigate weakly developable spaces. For a comparison with semi-metrizable spaces, we introduce and study a class of spaces among those of weakly developable spaces, semimetrizable spaces and first countable…

We characterize weak* closed unital vector spaces of operators on a Hilbert space $H$. More precisely, we first show that an operator system, which is the dual of an operator space, can be represented completely isometrically and weak*…

Several characterizations of weak cotype 2 and weak Hilbert spaces are given in terms of basis constants and other structural invariants of Banach spaces. For finite-dimensional spaces, characterizations depending on subspaces of fixed…

A completely entangled subspace of a tensor product of Hilbert spaces is a subspace with no non-trivial product vector. K. R. Parthasarathy determined the maximum dimension possible for such a subspace. Here we present a simple explicit…

We characterize the generalized Auslander--Reiten duality on the category of finitely presented modules over some certain Hom-finite category. Examples include the category FI of finite sets with injections, and the one VI of finite…

We explore the structure of the moduli space of vacua of Improved Bifundamentals, a recently introduced class of superconformal field theories. Utilizing the Hilbert Series, computed as a specific limit of the Superconformal Index, we…

The irreducible alternative superbimodules are studied. The complete classification is obtained for even bimodules of arbitrary dimension and for finite-dimensional irreducible superbimodules over an algebraically closed field.

Properties of partial integrals such as real and complex-valued polynomial, multiple polynomial, exponential, and conditional for ordinary differential systems are studied. The possibilities of constructing first integrals and last…

Hilbert evolution algebras generalize evolution algebras through a framework of Hilbert spaces. In this work we focus on infinite-dimensional Hilbert evolution algebras and their representation through a suitably defined weighted digraph.…

We make explicit in terms of categories a number of statements from the theory of partial inner product spaces (PIP spaces) and operators on them. In particular, we construct sheaves and cosheaves of operators on certain PIP spaces of…

We study the problem of constructing a contragredient functor on the category of admissible locally analytic representations of a p-adic analytic group G. A naive contragredient does not exist. As a best approximation, we construct an…

We extend the Horrocks correspondence between vector bundles and cohomology modules on the projective plane to the product of two projective lines. We introduce a set of invariants for a vector bundle on the product of two projective lines,…

We discuss Poincar\'e duality complexes X and the question whether or not their Spivak normal fibration admits a reduction to a vector bundle in the case where the dimension of X is at most 4. We show that in dimensions less than 4 such a…

The semi-tensor product (STP) of matrices is extended to the STP of hypermatrices. Some basic properties of the STP of matrices are extended to the STP of hypermatrices. The hyperdeterminant of hypersquares is introduced. Some algebraic and…

In this paper we want to revive the object sectional matrix which encodes the Hilbert functions of successive hyperplane sections of a homogeneous ideal. We translate and/or reprove recent results in this language. Moreover, some new…

This note aims to investigate the tensor product of two given Hilbert quasi *-algebras and its properties. The construction proposed in this note turns out to be again a Hilbert quasi *-algebra, thus interesting representability properties…

In this article, we present some results about Fourier multipliers on Hardy spaces in the product case. We mainly give descriptions of multipliers from the space $H^1(\mathbb{T}\times\mathbb{T})$ into the space $\ell^2$ and from the space…

We show that every (continuous) faithful product system admits a (continuous) faithful nondegenerate representation. For Hilbert spaces this is equivalent to Arveson's result that every Arveson system comes from an E_0-semigroup. We point…