WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 20, 2021
Successions of J-bessel in Spaces with Indefinite Metric
Authors: , ,
Abstract: A definition of Bessel’s sequences in spaces with an indefinite metric is introduced as a generalization
of Bessel’s sequences in Hilbert spaces. Moreover, a complete characterization of Bessel’s sequences in the
Hilbertspace associated to a space with an indefinite metric is given. The fundamental tools of Bessel’s sequences
theory are described in the formalism of spaces with an indefinite metric. It is shown how to construct a Bessel’s
sequences in spaces with an indefinite metric starting from a pair of Hilbert spaces, a condition is given to
decompose a Bessel’s sequences into in spaces with an indefinite metric so that this decomposition generates a
pair of Bessel’s sequences for the Hilbert spaces corresponding to the fundamental decomposition.
In spaces where there was no norm, it seemed impossible to construct Bessel’s sequences. The fact that in [1]
frame were constructed for Krein spaces motivated us to construct Bessel’s sequences for spaces of indefinite
metric.
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Pages: 144-151
DOI: 10.37394/23206.2021.20.15