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, Lp-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.
Antoine, J., & Trapani, C. (2019). Banach partial $*$-algebras: an overview. ADVANCES IN OPERATOR THEORY, 4(1), 71-98 [10.15352/aot.1802-1312].
Data di pubblicazione: | 2019 | |
Titolo: | Banach partial $*$-algebras: an overview | |
Autori: | ||
Citazione: | Antoine, J., & Trapani, C. (2019). Banach partial $*$-algebras: an overview. ADVANCES IN OPERATOR THEORY, 4(1), 71-98 [10.15352/aot.1802-1312]. | |
Rivista: | ||
Digital Object Identifier (DOI): | http://dx.doi.org/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, Lp-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. | |
Settore Scientifico Disciplinare: | Settore MAT/05 - Analisi Matematica | |
Appare nelle tipologie: | 1.01 Articolo in rivista |
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