Unbounded derivations and *-automorphisms groups of Banach quasi *-algebras
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This paper is devoted to the study of unbounded derivations on Banach quasi *-algebras with a particular emphasis to the case when they are infinitesimal generators of one-parameter automorphisms groups. Both of them, derivations and automorphisms are considered in a weak sense, i.e., with the use of a certain families of bounded sesquilinear forms. Conditions for a weak *-derivation to be the generator of a *-automorphisms group are given.
KeywordsBanach quasi *-algebras Unbounded derivations *-Automorphisms groups and their infinitesimal generators Integrability of derivation
Mathematics Subject ClassificationPrimary 46L57 Secondary 46L08, 47L60
This work has been done in the framework of the Project “Alcuni aspetti di teoria spettrale di operatori e di algebre; frames in spazi di Hilbert rigged”, INDAM-GNAMPA 2018. The first author wishes to thank prof. M. Fragoulopoulou for her valuable suggestions and the Department of Mathematics of National and Kapodistrian University of Athens in Greece for its hospitality.
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