### Banach partial $*$-algebras: an overview

#### 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.

#### Article information

Source
Adv. Oper. Theory, Volume 4, Number 1 (2019), 71-98.

Dates
Accepted: 14 March 2018
First available in Project Euclid: 4 April 2018

https://projecteuclid.org/euclid.aot/1522807289

Digital Object Identifier
doi:10.15352/aot.1802-1312

Mathematical Reviews number (MathSciNet)
MR3867335

Zentralblatt MATH identifier
06946444

#### Citation

Antoine, J.-P.; Trapani, C. Banach partial $*$-algebras: an overview. Adv. Oper. Theory 4 (2019), no. 1, 71--98. doi:10.15352/aot.1802-1312. https://projecteuclid.org/euclid.aot/1522807289

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