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On Fréchet–Hilbert algebras

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Abstract

We consider Hilbert algebras with a supplementary Fréchet topology and get various extensions of the algebraic structure by using duality techniques. In particular we obtain optimal multiplier-type involutive algebras which in applications are large enough to be of significant practical use. The setting covers many situations arising from quantization rules, as those involving square-integrable families of bounded operators

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de Chile, Las Palmeras 3425, Casilla, 653, Santiago, Chile

    M. Măntoiu

  2. Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, Bucharest, Romania

    R. Purice

Authors
  1. M. Măntoiu
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  2. R. Purice
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Correspondence to M. Măntoiu.

Additional information

The authors have been supported by the Chilean Science Foundation Fondecyt under the Grant 1120300. RP acknowledges the partial support of a grant of the Romanian National Authority for Scientific Research, CNCS-UEFISCDI, project number PN-II-ID-PCE-2011-3-0131 and the hospitality of the Universidad de Chile where part of this work has been done.

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Măntoiu, M., Purice, R. On Fréchet–Hilbert algebras. Arch. Math. 103, 157–166 (2014). https://doi.org/10.1007/s00013-014-0675-8

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  • DOI: https://doi.org/10.1007/s00013-014-0675-8

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