Search results for " Sesquilinear forms"

showing 4 items of 4 documents

Extensions of Representable Positive Linear Functionals to Unitized Quasi *-Algebras: A New Method

2014

In this paper we introduce a topological approach for extending a representable linear functional \({\omega}\), defined on a topological quasi *-algebra without unit, to a representable linear functional defined on a quasi *-algebra with unit. In particular, we suppose that \({\omega}\) is continuous and the positive sesquilinear form \({\varphi_\omega}\), associated with \({\omega}\), is closable and prove that the extension \({\overline{\varphi_\omega}^e}\) of the closure \({\overline{\varphi_\omega}}\) is an i.p.s. form. By \({\overline{\varphi_\omega}^e}\) we construct the desired extension.

CombinatoricsClosure (mathematics)Sesquilinear formSettore MAT/05 - Analisi MatematicaGeneral MathematicsLinear formExtension (predicate logic)Algebra over a fieldinvariant sesquilinear positive forms closable positive sesquilinear forms unitized quasi *-algebrasOmegaUnit (ring theory)Mathematics
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Closedness and lower semicontinuity of positive sesquilinear forms

2009

The relationship between the notion of closedness, lower semicontinuity and completeness (of a quotient) of the domain of a positive sesquilinear form defined on a subspace of a topological vector space is investigated and sufficient conditions for their equivalence are given.

Discrete mathematicsMathematics::Functional AnalysisPure mathematicsMathematics::Operator AlgebrasSesquilinear formGeneral MathematicsMathematics::Optimization and ControlMathematics::General TopologyClosedness Semicontinuity Sesquilinear formsDomain (mathematical analysis)Topological vector spaceSettore MAT/05 - Analisi MatematicaAlgebra over a fieldCompleteness (statistics)Equivalence (measure theory)Subspace topologyQuotientMathematicsRendiconti del Circolo Matematico di Palermo
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A survey on solvable sesquilinear forms

2018

The aim of this paper is to present a unified theory of many Kato type representation theorems in terms of solvable forms on a Hilbert space \((H,\langle\cdot,\cdot\rangle)\) In particular, for some sesquilinear forms Ω on a dense domain \(D\subseteq\mathcal {H}\) one looks for a representation \(\Omega(\xi,\eta)= \langle T\xi,\eta\rangle\) \((\xi\epsilon\mathcal{D}\mathcal(T),\eta\epsilon D)\) where T is a densely defined closed operator with domain \(D(\mathcal{T})\subseteq \mathcal{D}\). There are two characteristic aspects of a solvable form on H. One is that the domain of the form can be turned into a reexive Banach space that need not be a Hilbert space. The second one is that represe…

Operator (physics)Banach spaceHilbert spaceKato’s representation theoremType (model theory)Combinatoricssymbols.namesakeSettore MAT/05 - Analisi MatematicaProduct (mathematics)Bounded functionDomain (ring theory)symbolsQ-closed and solvable sesquilinear formsUnified field theoryMathematics
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A note on *-derivations of partial *-algebras

2012

A definition of *-derivation of partial *-algebra through a sufficient family of ips-forms is proposed.

partial *-algebras sesquilinear forms *-derivationSettore MAT/05 - Analisi Matematica
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