Open AccessBesselian g-frames and near g-Riesz bases
Author(s) -
Mohammad Reza Abdollahpour,
Abbas Najati
Publication year - 2011
Publication title -
applicable analysis and discrete mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.69
H-Index - 26
eISSN - 2406-100X
pISSN - 1452-8630
DOI - 10.2298/aadm110510013a
Subject(s) - mathematics , orthonormal basis , basis (linear algebra) , riesz representation theorem , riesz transform , m. riesz extension theorem , hilbert space , kernel (algebra) , riesz potential , orthogonal basis , pure mathematics , frame (networking) , operator (biology) , geometry , computer science , telecommunications , physics , quantum mechanics , biochemistry , chemistry , repressor , transcription factor , gene
In this paper we introduce and study near g-Riesz basis, Besselian g-frames and unconditional g-frames. We show that a near g-Riesz basis is a Besselian g-frame and we conclude that under some conditions the kernel of associated synthesis operator for a near g-Riesz basis is finite dimensional. Finally, we show that a g-frame is a g-Riesz basis for a Hilbert space H if and only if there is an equivalent inner product on H, with respect to which it becomes an g-orthonormal basis for H