A+ CATEGORY SCIENTIFIC UNIT

Factorizing multilinear operators on Banach spaces, $C^{*}$-algebras and $JB^{*}$-triples

Volume 192 / 2009

Carlos Palazuelos, Antonio M. Peralta, Ignacio Villanueva Studia Mathematica 192 (2009), 129-146 MSC: Primary 46G25, 47H60, 47B10, 46L05, 17C65, 46L70. DOI: 10.4064/sm192-2-3

Abstract

In recent papers, the Right and the Strong$^*$ topologies have been introduced and studied on general Banach spaces. We characterize different types of continuity for multilinear operators (joint, uniform, etc.) with respect to the above topologies. We also study the relations between them. Finally, in the last section, we relate the joint Strong$^{*}$-to-norm continuity of a multilinear operator $T$ defined on $C^{*}$-algebras (respectively, $JB^{*}$-triples) to $C^{*}$-summability (respectively, $JB^*$-triple-summability).

Authors

  • Carlos PalazuelosDepartamento de Análisis Matemático
    Facultad de Matemáticas
    Universidad Complutense de Madrid
    28040 Madrid, Spain
    e-mail
  • Antonio M. PeraltaDepartamento de Análisis Matemático
    Facultad de Ciencias
    Universidad de Granada
    18071 Granada, Spain
    e-mail
  • Ignacio VillanuevaDepartamento de Análisis Matemático
    Facultad de Matemáticas
    Universidad Complutense de Madrid
    28040 Madrid, Spain
    e-mail

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