Old and new results on Allan's GB*-algebras

• Autorzy: Maria Fragoulopoulou , Atsushi Inoue , Klaus-Detlef Kürsten
• Języki publikacji: EN

Abstrakty

EN

This is an expository paper on the importance and applications of GB*-algebras in the theory of unbounded operators, which is closely related to quantum field theory and quantum mechanics. After recalling the definition and the main examples of GB*-algebras we exhibit their most important properties. Then, through concrete examples we are led to a question concerning the structure of the completion of a given C*-algebra 𝓐₀[||·||₀], under a locally convex *-algebra topology τ, making the multiplication of 𝓐₀ jointly continuous. We conclude that such a completion is a GB*-algebra over the τ-closure of the unit ball of 𝓐₀[||·||₀]. Further, we discuss some consequences of this result; we briefly comment the case when τ makes the multiplication of 𝓐₀ separately continuous and illustrate the results by examples.

Kategorie tematyczne

• 47L60: Algebras of unbounded operators; partial algebras of operators
• 46H20: Structure, classification of topological algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2010
• Tom: 91
• Numer: 1
• Strony: 169-178

Daty

wydano

2010

Twórcy

autor

Maria Fragoulopoulou

• Department of Mathematics, University of Athens, Panepistimiopolis, Athens 15784, Greece

autor

Atsushi Inoue

• Department of Applied Mathematics, Fukuoka University, Nanakuma, Jonan-ku, Fukuoka 814-0180, Japan

autor

Klaus-Detlef Kürsten

• Mathematisches Institut, Universität Leipzig, Johannisgasse 26, D-04103 Leipzig, Germany

Identyfikatory

DOI

10.4064/bc91-0-9