*-Representations, seminorms and structure properties of normed quasi *-algebras

Camillo Trapani

Studia Mathematica (2008)

  • Volume: 186, Issue: 1, page 47-75
  • ISSN: 0039-3223

Abstract

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The class of *-representations of a normed quasi *-algebra (𝔛,𝓐₀) is investigated, mainly for its relationship with the structure of (𝔛,𝓐₀). The starting point of this analysis is the construction of GNS-like *-representations of a quasi *-algebra (𝔛,𝓐₀) defined by invariant positive sesquilinear forms. The family of bounded invariant positive sesquilinear forms defines some seminorms (in some cases, C*-seminorms) that provide useful information on the structure of (𝔛,𝓐₀) and on the continuity properties of its *-representations.

How to cite

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Camillo Trapani. "*-Representations, seminorms and structure properties of normed quasi *-algebras." Studia Mathematica 186.1 (2008): 47-75. <http://eudml.org/doc/285279>.

@article{CamilloTrapani2008,
abstract = {The class of *-representations of a normed quasi *-algebra (𝔛,𝓐₀) is investigated, mainly for its relationship with the structure of (𝔛,𝓐₀). The starting point of this analysis is the construction of GNS-like *-representations of a quasi *-algebra (𝔛,𝓐₀) defined by invariant positive sesquilinear forms. The family of bounded invariant positive sesquilinear forms defines some seminorms (in some cases, C*-seminorms) that provide useful information on the structure of (𝔛,𝓐₀) and on the continuity properties of its *-representations.},
author = {Camillo Trapani},
journal = {Studia Mathematica},
keywords = {quasi *-algebra; *-representation; GNS-construction; positive sesquilinear form},
language = {eng},
number = {1},
pages = {47-75},
title = {*-Representations, seminorms and structure properties of normed quasi *-algebras},
url = {http://eudml.org/doc/285279},
volume = {186},
year = {2008},
}

TY - JOUR
AU - Camillo Trapani
TI - *-Representations, seminorms and structure properties of normed quasi *-algebras
JO - Studia Mathematica
PY - 2008
VL - 186
IS - 1
SP - 47
EP - 75
AB - The class of *-representations of a normed quasi *-algebra (𝔛,𝓐₀) is investigated, mainly for its relationship with the structure of (𝔛,𝓐₀). The starting point of this analysis is the construction of GNS-like *-representations of a quasi *-algebra (𝔛,𝓐₀) defined by invariant positive sesquilinear forms. The family of bounded invariant positive sesquilinear forms defines some seminorms (in some cases, C*-seminorms) that provide useful information on the structure of (𝔛,𝓐₀) and on the continuity properties of its *-representations.
LA - eng
KW - quasi *-algebra; *-representation; GNS-construction; positive sesquilinear form
UR - http://eudml.org/doc/285279
ER -

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