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Winter 2019 Banach partial $*$-algebras: an overview
J.-P. Antoine, C. Trapani
Adv. Oper. Theory 4(1): 71-98 (Winter 2019). DOI: 10.15352/aot.1802-1312

Abstract

A Banach partial $*$-algebra is a locally convex partial $*$-algebra whose total space is a Banach space. A Banach partial $*$-algebra is said to be of type (B) if it possesses a generating family of multiplier spaces that are also Banach spaces. We describe the basic properties of these objects and display a number of examples, namely, $L^p$-like function spaces and spaces of operators on Hilbert scales or lattices. Finally we analyze the important cases of Banach quasi $*$-algebras and $CQ^*$-algebras.

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J.-P. Antoine. C. Trapani. "Banach partial $*$-algebras: an overview." Adv. Oper. Theory 4 (1) 71 - 98, Winter 2019. https://doi.org/10.15352/aot.1802-1312

Information

Received: 13 February 2018; Accepted: 14 March 2018; Published: Winter 2019
First available in Project Euclid: 4 April 2018

zbMATH: 06946444
MathSciNet: MR3867335
Digital Object Identifier: 10.15352/aot.1802-1312

Subjects:
Primary: 08A55
Secondary: 46J10, 47L60

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.4 • No. 1 • Winter 2019
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