A Characterization of Schauder Frames Which Are Near-schauder Bases
نویسندگان
چکیده
A basic problem of interest in connection with the study of Schauder frames in Banach spaces is that of characterizing those Schauder frames which can essentially be regarded as Schauder bases. In this paper, we study this problem using the notion of a minimal-associated sequence space and a minimal-associated reconstruction operator for Schauder frames. We prove that a Schauder frame is a near-Schauder basis if and only if the kernel of the minimal-associated reconstruction operator contains no copy of c0. In particular, a Schauder frame of a Banach space with no copy of c0 is a near-Schauder basis if and only if the minimal-associated sequence space contains no copy of c0. In these cases, the minimal-associated reconstruction operator has a finite dimensional kernel and the dimension of the kernel is exactly the excess of the Schauder frame.
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