Besselian g-frames and near g-Riesz bases | Zendy

Mohammad Reza Abdollahpour | Zendy; Abbas Najati | Zendy

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Besselian 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

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