G-vector-valued Sequence Space Frames

G-vector-valued sequence space frames and g-Banach frames for Banach spaces are introduced and studied in this paper. Also, the concepts of duality mapping and ${\beta}$-dual of a BK-space are used to define frame mapping and synthesis operator of these frames, respectively. Finally, some results re...

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Veröffentlicht in:Kyungpook mathematical journal 2016, 56(3), , pp.793-806
1. Verfasser: Osgooei, Elnaz
Format: Artikel
Sprache:eng
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Zusammenfassung:G-vector-valued sequence space frames and g-Banach frames for Banach spaces are introduced and studied in this paper. Also, the concepts of duality mapping and ${\beta}$-dual of a BK-space are used to define frame mapping and synthesis operator of these frames, respectively. Finally, some results regarding the existence of g-vector-valued sequence space frames and g-Banach frames are obtained. In particular, it is proved that if X is a separable Banach space and Y is a Banach space with a Schauder basis, then there exist a Y-valued sequence space $Y_v$ and a g-Banach frame for X with respect to Y and $Y_v$.
ISSN:1225-6951
0454-8124
DOI:10.5666/KMJ.2016.56.3.793