Generalized B\({}^∗\)-algebras: An introduction

Generalized B\({}^{∗}\)-algebras (GB\({}^{∗}\)-algebras, for short) are locally convex \(∗\)-algebras which are abstract \(∗\)-algebras of unbounded linear operators on a Hilbert space, and are generalisations of C\({}^{∗}\)-algebras. They were first studied by G. R. Allan in the late sixties, and then later, in the early seventies, by P. G. Dixon to include non locally convex algebras. The aim of this talk is to give an introduction of these algebras and unbounded operator algebras. We also give some results of the speaker and his collaborators, including some connections between GB\({}^{∗}\)- algebras and mathematical physics.

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