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

Risultato della ricerca: Article

Abstract

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, is introduced. In particular, we suppose that $\omega$ is continuous and the positive sesquilinear form $\vom$, associated to $\omega$, is closable and prove that the extension $\overline{\vom}^e$ of the closure $\overline{\vom}$ is an i.p.s. form. By $\overline{\vom}^e$ we construct the desired extension.
Lingua originaleEnglish
pagine (da-a)997-1008
Numero di pagine12
RivistaMediterranean Journal of Mathematics
Volume12
Stato di pubblicazionePublished - 2015

Fingerprint

Linear Functionals
Linear Functional
Sesquilinear form
Algebra
Unit
Closure
Form

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cita questo

@article{d43b43d7f233498596604e7e93564455,
title = "Extensions of Representable Positive Linear Functionals to Unitized Quasi *-Algebras: A New Method",
abstract = "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, is introduced. In particular, we suppose that $\omega$ is continuous and the positive sesquilinear form $\vom$, associated to $\omega$, is closable and prove that the extension $\overline{\vom}^e$ of the closure $\overline{\vom}$ is an i.p.s. form. By $\overline{\vom}^e$ we construct the desired extension.",
author = "Giorgia Bellomonte",
year = "2015",
language = "English",
volume = "12",
pages = "997--1008",
journal = "Mediterranean Journal of Mathematics",
issn = "1660-5446",
publisher = "Birkhauser Verlag Basel",

}

TY - JOUR

T1 - Extensions of Representable Positive Linear Functionals to Unitized Quasi *-Algebras: A New Method

AU - Bellomonte, Giorgia

PY - 2015

Y1 - 2015

N2 - 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, is introduced. In particular, we suppose that $\omega$ is continuous and the positive sesquilinear form $\vom$, associated to $\omega$, is closable and prove that the extension $\overline{\vom}^e$ of the closure $\overline{\vom}$ is an i.p.s. form. By $\overline{\vom}^e$ we construct the desired extension.

AB - 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, is introduced. In particular, we suppose that $\omega$ is continuous and the positive sesquilinear form $\vom$, associated to $\omega$, is closable and prove that the extension $\overline{\vom}^e$ of the closure $\overline{\vom}$ is an i.p.s. form. By $\overline{\vom}^e$ we construct the desired extension.

UR - http://hdl.handle.net/10447/97509

UR - http://link.springer.com/article/10.1007/s00009-014-0432-z

M3 - Article

VL - 12

SP - 997

EP - 1008

JO - Mediterranean Journal of Mathematics

JF - Mediterranean Journal of Mathematics

SN - 1660-5446

ER -