Banach partial \(^*\)-algebras: an overview. (English) Zbl 1420.46040

Summary: 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.


46J10 Banach algebras of continuous functions, function algebras
47L60 Algebras of unbounded operators; partial algebras of operators
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