Sesquilinear forms associated to sequences on Hilbert spaces

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2 Citazioni (Scopus)

Abstract

The possibility of defining sesquilinear forms starting from one or two sequences of elements of a Hilbert space is investigated. One can associate operators to these forms and in particular look for conditions to apply representation theorems of sesquilinear forms, such as Kato’s theorems. The associated operators correspond to classical frame operators or weakly-defined multipliers in the bounded context. In general some properties of them, such as the invertibility and the resolvent set, are related to properties of the sesquilinear forms. As an upshot of this approach new features of sequences (or pairs of sequences) which are semi-frames (or reproducing pairs) are obtained.
Lingua originaleEnglish
pagine (da-a)625-650
Numero di pagine26
RivistaMONATSHEFTE FÜR MATHEMATIK
Volume189
Stato di pubblicazionePublished - 2019

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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