Banach partial $*$-algebras: an overview

Camillo Trapani, Jean-Pierre Antoine

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Abstract

A Banach partial *-algebra is a locally convex partial *-algebrawhose total space is a Banach space. A Banach partial *-algebra is said to beof type (B) if it possesses a generating family of multiplier spaces that are alsoBanach spaces. We describe the basic properties of these objects and displaya number of examples, namely, Lp-like function spaces and spaces of operatorson Hilbert scales or lattices. Finally we analyze the important cases of Banachquasi *-algebras and CQ-algebras.
Lingua originaleEnglish
pagine (da-a)71-98
Numero di pagine28
RivistaAdvances in Operator Theory
Volume4
Stato di pubblicazionePublished - 2019

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All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Analysis

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