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2013•Kyungpook mathematical journalOpen access

G-frames as Sums of Some g-orthonormal Bases

Mohammad Reza Abdollahpour, Abbas Najati

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Abstract

In this paper we show that a g-frame for a Hilbert space H can be written as a linear combination of two g-orthonormal bases for H if and only if it is a g-Riesz basis for H. Also, we show that every g-frame for a Hilbert space H is a multiple of a sum of three g-orthonormal bases for H.Definition 1.1.We call a sequence {Λ i ∈ B(H, H i ) : i ∈ I} a g-frame for H with

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In this paper we show that a g-frame for a Hilbert space H can be written as a linear combination of two g-orthonormal bases for H if and only if it is a g-Riesz basis for H. Also, we show that every g-frame for a Hilbert space H is a multiple of a sum of three g-orthonormal bases for H.Definition 1.1.We call a sequence {Λ i ∈ B(H, H i ) : i ∈ I} a g-frame for H with

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Available abstract

In this paper we show that a g-frame for a Hilbert space H can be written as a linear combination of two g-orthonormal bases for H if and only if it is a g-Riesz basis for H. Also, we show that every g-frame for a Hilbert space H is a multiple of a sum of three g-orthonormal bases for H.Definition 1.1.We call a sequence {Λ i ∈ B(H, H i ) : i ∈ I} a g-frame for H with

Key concepts: Orthonormal basis, Mathematics, Hilbert space, Basis (linear algebra), Frame (networking), Pure mathematics, Riesz representation theorem, Space (punctuation)

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