TY - JOUR
ID - 59546
T1 - Banach partial $*$-algebras: an overview
JO - Advances in Operator Theory
JA - AOT
LA - en
SN -
A1 - Antoine, Jean-Pierre
A1 - Trapani, Camillo
Y1 - 2019
PY - 2019/01/01
VL - 4
IS - 1
SP - 71
EP - 98
KW - Partial *-algebra
KW - Banach partial *-algebra
KW - CQ*-algebra
KW - partial inner product space
KW - operators on Hilbert scale
DO - 10.15352/aot.1802-1312
N2 - 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.
UR - http://www.aot-math.org/article_59546.html
L1 - http://www.aot-math.org/pdf_59546_efe8b77c9db76ad477be01c5ecb23564.html
ER -