G-frames and their generalized multipliers in Hilbert spaces

Hosseinnezhad, Hessam; Tabadkan, Gholamreza Abbaspour; Rahimi, Asghar

doi:10.1215/20088752-2018-0017

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“…for all x ∈ H. As usual, the sequence Λ := {Λ i S −1 Λ } i∈I is called the canonical dual g-frame of Λ which is a g-frame for H with frame operator S −1 Λ and frame bounds B −1 Λ and A −1 Λ . Finally, we recall from [6] that for two g-Bessel sequences Λ and Γ and a bounded operator U :…”

Section: Preliminariesmentioning

confidence: 99%

Invertibility of generalized g-frame multipliers in Hilbert spaces

Abolghasemi¹,

Tolooei²,

Moosavianfard³

2019

Preprint

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In this paper, we investigate the invertibility of generalized g-Bessel multipliers. We show that for semi-normalized symbols, the inverse of any invertible generalized g-frame multiplier can be represented as a generalized g-frame multiplier. Also we give several approaches for constructing invertible generalized g-frame multipliers from the given one. It is worth mentioning that some of our results are quite different from those studied in the previous literatures on this topic. 2010 MSC : 42C15, 47A05, 41A58.

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Section: Preliminariesmentioning

confidence: 99%