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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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