Hilbert-Schauder Frame Operators

2012/06/27 by Liu, Rui
#46B #47A #47B #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1206.6146

Abstract

We introduce a new concept of frame operators for Banach spaces we call a Hilbert-Schauder frame operator. This is a hybird between standard frame theory for Hilbert spaces and Schauder frame theory for Banach spaces. Most of our results involve basic structure properties of the Hilbert-Schauder frame operator. Examples of Hilbert-Schauder frames include standard Hilbert frames and classical bases of ℓ_p and L^p-spaces with 1< p ≤ 2. Finally, we give a new isomorphic characterization of Hilbert spaces.

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