Advances in Operator Theory

Banach partial $*$-algebras: an overview

J.-P. Antoine and C. Trapani

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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.

Article information

Adv. Oper. Theory, Volume 4, Number 1 (2019), 71-98.

Received: 13 February 2018
Accepted: 14 March 2018
First available in Project Euclid: 4 April 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 08A55: Partial algebras
Secondary: 46J10: Banach algebras of continuous functions, function algebras [See also 46E25] 47L60: Algebras of unbounded operators; partial algebras of operators

partial $*$-algebra Banach partial $*$-algebra $CQ^*$-algebra partial inner product space operators on Hilbert scale


Antoine, J.-P.; Trapani, C. Banach partial $*$-algebras: an overview. Adv. Oper. Theory 4 (2019), no. 1, 71--98. doi:10.15352/aot.1802-1312.

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