ERRATUM: "FRAMES OF SUBSPACES FOR BANACH SPACES"

Frames for Banach Spaces

We use several fundamental results which characterize frames for a Hilbert space to give natural generalizations of Hilbert space frames to general Banach spaces. However, we will see that all of these natural generalizations (as well as the currently used generalizations) are equivalent to properties already extensively developed in Banach space theory. We show that the dilation characterizati...

On quasi-complemented subspaces of banach spaces.

Banach frames for α-modulation spaces

This paper is concerned with the characterization of α-modulation spaces by Banach frames, i.e., stable and redundant nonorthogonal expansions, constituted of functions obtained by a suitable combination of translation, modulation and dilation of a mother atom. In particular, the parameter α ∈ [0,1] governs the dependence of the dilation factor on the frequency. The result is achieved by exploi...

Banach Λ-Frames for Operator Spaces

The Banach frame for a Banach space  can reconstruct each vector in  by the pre-frame operator or the reconstruction operator. The Banach Λ-frame for operator spaces was introduced by Kaushik, Vashisht and Khattar [Reconstruction Property and Frames in Banach Spaces, Palestine Journal of Mathematics, 3(1), 2014, 11-26]. In this paper we give necessary and sufficient conditions for the existen...

Coefficient Quantization for Frames in Banach Spaces

Let (ei) be a fundamental system of a Banach space. We consider the problem of approximating linear combinations of elements of this system by linear combinations using quantized coefficients. We will concentrate on systems which are possibly redundant. Our model for this situation will be frames in Banach spaces.