Unconditionally convergent multipliers and Bessel sequences

We prove that every unconditionally summable sequence in a Hilbert space can be factorized as the product of a square summable scalar sequence and a Bessel sequence. Some consequences on the representation of unconditionally convergent multipliers are obtained, thus providing positive answers to a c...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 455; no. 1; pp. 389 - 395
Main Authors Fernández, Carmen, Galbis, Antonio, Primo, Eva
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.11.2017
Subjects
Bessel sequence
Multiplier
Unconditional convergence
Bessel sequence
Multiplier
Unconditional convergence
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Summary:We prove that every unconditionally summable sequence in a Hilbert space can be factorized as the product of a square summable scalar sequence and a Bessel sequence. Some consequences on the representation of unconditionally convergent multipliers are obtained, thus providing positive answers to a conjecture by Balazs and Stoeva in some particular cases.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2017.05.054