Frames, Riesz bases, and sampling expansions in Banach spaces via semi-inner products

A characterization of L-dual frames and L-dual Riesz bases

This paper is an investigation of $L$-dual frames with respect to a function-valued inner product, the so called $L$-bracket product on $L^{2}(G)$, where G is a locally compact abelian group with a uniform lattice $L$. We show that several well known theorems for dual frames and dual Riesz bases in a Hilbert space remain valid for $L$-dual frames and $L$-dual Riesz bases in $L^{2}(G)$.

Some Results concerning Riesz Bases and Frames in Banach Spaces

In this paper, we give characterizations of Riesz bases and near Riesz bases in Banach spaces. The notion of atomic system is defined and a characterization of atomic system has been given. Also results exhibiting relationship between frames, atomic systems and Riesz bases have been proved. Further, we show that every atomic system is a projection of a Riesz basis in Banach spaces. Finally, we ...

G-Frames, g-orthonormal bases and g-Riesz bases

G-Frames in Hilbert spaces are a redundant set of operators which yield a representation for each vector in the space. In this paper we investigate the connection between g-frames, g-orthonormal bases and g-Riesz bases. We show that a family of bounded operators is a g-Bessel sequences if and only if the Gram matrix associated to its denes a bounded operator.

Perturbation of frames in Banach spaces

In this paper we consider perturbation of Xd-Bessel sequences, Xdframes, Banach frames, atomic decompositions and Xd-Riesz bases in separable Banach spaces. Equivalence between some perturbation conditions is investigated.

Generalized Frames in Hilbert Spaces