%0 Journal Article
%T Banach partial $*$-algebras: an overview
%J Advances in Operator Theory
%I Tusi Mathematical Research Group (TMRG)
%Z 2538-225X
%A Antoine, Jean-Pierre
%A Trapani, Camillo
%D 2019
%\ 01/01/2019
%V 4
%N 1
%P 71-98
%! Banach partial $*$-algebras: an overview
%K Partial *-algebra
%K Banach partial *-algebra
%K CQ*-algebra
%K partial inner product space
%K operators on Hilbert scale
%R 10.15352/aot.1802-1312
%X 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.
%U http://www.aot-math.org/article_59546_efe8b77c9db76ad477be01c5ecb23564.pdf