A+ CATEGORY SCIENTIFIC UNIT

Bounded elements in certain topological partial $^*$-algebras

Volume 203 / 2011

Jean-Pierre Antoine, Camillo Trapani, Francesco Tschinke Studia Mathematica 203 (2011), 223-251 MSC: Primary 47L60; Secondary 46H15. DOI: 10.4064/sm203-3-2

Abstract

We continue our study of topological partial $^*$-algebras, focusing on the interplay between various partial multiplications. The special case of partial $^*$-algebras of operators is examined first, in particular the link between strong and weak multiplications, on one hand, and invariant positive sesquilinear (ips) forms, on the other. Then the analysis is extended to abstract topological partial $^*$-algebras, emphasizing the crucial role played by appropriate bounded elements, called $\cal M$-bounded. Finally, some remarks are made concerning representations in terms of so-called partial $GC^*$-algebras of operators.

Authors

  • Jean-Pierre AntoineInstitut de Recherche
    en Mathématique et Physique
    Université Catholique de Louvain
    B-1348 Louvain-la-Neuve, Belgium
    e-mail
  • Camillo TrapaniDipartimento di Matematica e Informatica
    Università di Palermo
    I-90123 Palermo, Italy
    e-mail
  • Francesco TschinkeDipartimento di Metodi e Modelli Matematici
    Facoltà d'Ingegneria
    Università di Palermo
    I-90128 Palermo, Italy
    e-mail

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