# Banach partial $*$-algebras‎: ‎an overview

Document Type: Special issue: Trends in Operators on Banach Spaces

Authors

1 Universit&amp;eacute; catholique de Louvain - IRMP

2 Dipartimento di Matematica e Informatica, Universit&agrave; di Palermo

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.

Keywords

### History

• Receive Date: 13 February 2018
• Revise Date: 14 March 2018
• Accept Date: 14 March 2018