Lower Semi-frames, Frames, and Metric Operators

Camillo Trapani, Rosario Corso, Jean-Pierre Antoine

Risultato della ricerca: Articlepeer review

Abstract

This paper deals with the possibility of transforming a weakly measurable function in a Hilbert space into a continuous frame by a metric operator, i.e., a strictly positive self-adjoint operator. A necessary condition is that the domain of the analysis operator associated with the function be dense. The study is done also with the help of the generalized frame operator associated with a weakly measurable function, which has better properties than the usual frame operator. A special attention is given to lower semi-frames: indeed, if the domain of the analysis operator is dense, then a lower semi-frame can be transformed into a Parseval frame with a (special) metric operator.
Lingua originaleEnglish
pagine (da-a)1-20
Numero di pagine20
RivistaMediterranean Journal of Mathematics
Volume18
Stato di pubblicazionePublished - 2021

All Science Journal Classification (ASJC) codes

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