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Volume 33, Issue 2
New Characterizations of Operator-Valued Bases on Hilbert Spaces

M. S. Asgari

DOI: 10.4208/ata.2017.v33.n2.6

Anal. Theory Appl., 33 (2017), pp. 157-177.

Published online: 2017-05

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  • Abstract

In this paper we study operator valued bases on Hilbert spaces and similar to Schauder bases theory we introduce characterizations of this generalized bases in Hilbert spaces. We redefine the dual basis associated with a generalized basis and prove that the operators of a dual $g$-basis are continuous. Finally we consider the stability of $g$-bases under small perturbations. We generalize two results of Krein-Milman-Rutman and Paley-Wiener [7] to the situation of $g$-basis.

  • Keywords

$g$-bases, dual $g$-bases, $g$-biorthogonal sequence.

  • AMS Subject Headings

41A58, 42C15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-33-157, author = {M. S. Asgari}, title = {New Characterizations of Operator-Valued Bases on Hilbert Spaces}, journal = {Analysis in Theory and Applications}, year = {2017}, volume = {33}, number = {2}, pages = {157--177}, abstract = {

In this paper we study operator valued bases on Hilbert spaces and similar to Schauder bases theory we introduce characterizations of this generalized bases in Hilbert spaces. We redefine the dual basis associated with a generalized basis and prove that the operators of a dual $g$-basis are continuous. Finally we consider the stability of $g$-bases under small perturbations. We generalize two results of Krein-Milman-Rutman and Paley-Wiener [7] to the situation of $g$-basis.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2017.v33.n2.6}, url = {http://global-sci.org/intro/article_detail/ata/10043.html} }
TY - JOUR T1 - New Characterizations of Operator-Valued Bases on Hilbert Spaces AU - M. S. Asgari JO - Analysis in Theory and Applications VL - 2 SP - 157 EP - 177 PY - 2017 DA - 2017/05 SN - 33 DO - http://doi.org/10.4208/ata.2017.v33.n2.6 UR - https://global-sci.org/intro/article_detail/ata/10043.html KW - $g$-bases, dual $g$-bases, $g$-biorthogonal sequence. AB -

In this paper we study operator valued bases on Hilbert spaces and similar to Schauder bases theory we introduce characterizations of this generalized bases in Hilbert spaces. We redefine the dual basis associated with a generalized basis and prove that the operators of a dual $g$-basis are continuous. Finally we consider the stability of $g$-bases under small perturbations. We generalize two results of Krein-Milman-Rutman and Paley-Wiener [7] to the situation of $g$-basis.

M. S. Asgari. (2017). New Characterizations of Operator-Valued Bases on Hilbert Spaces. Analysis in Theory and Applications. 33 (2). 157-177. doi:10.4208/ata.2017.v33.n2.6
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