In this paper, we introduce the concept of $g$-dual frames for Hilbert $C^{*}$-modules, and then the properties and stability results of $g$-dual frames  are given.  A characterization of $g$-dual frames, approximately dual frames and dual frames of a given frame is established. We also give some examples to show that the characterization of $g$-dual frames for Riesz bases in Hilbert spaces is ...

 In network code setting, a constant dimension code is a set of k-dimensional subspaces of F nq . If F_q n is a nondegenerated symlectic vector space with bilinear form f, an isotropic subspace U of F n q is a subspace that for all x, y ∈ U, f(x, y) = 0. We introduce isotropic subspace codes simply as a set of isotropic subspaces and show how the isotropic property use in decoding process, then...

Fusion frame theory is an emerging mathematical theory that provides a natural framework for performing hierarchical data processing. A fusion frame can be regarded as a frame-like collection of subspaces in a Hilbert Communicated by Qiyu Sun. P.G.C. and A.H. were supported by NSF DMS 0704216. G.K. would like to thank the Department of Statistics at Stanford University and the Mathematics Depar...

The theory of  continuous frames in Hilbert spaces is extended, by using the concepts of measure spaces, in order to get the results of a new application of operator theory.  The $K$-frames were  introduced by G$breve{mbox{a}}$vruta (2012) for Hilbert spaces to study atomic systems with respect to a bounded linear operator. Due to the structure of  $K$-frames, there are many differences between...

$K$-frames which are generalization of frames on Hilbert spaces‎, ‎were introduced‎ ‎to study atomic systems with respect to a bounded linear operator‎. ‎In this paper‎, ‎$*$-$K$-frames on Hilbert $C^*$-modules‎, ‎as a generalization of $K$-frames‎, ‎are introduced and some of their properties are obtained‎. ‎Then some relations‎ ‎between $*$-$K$-frames and $*$-atomic systems with respect to a...

Fusion frames are valuable generalizations of discrete frames. Most concepts of fusion frames are shared by discrete frames. However, the dual setting is so complicated. In particular, unlike discrete frames, two fusion frames are not dual of each other in general. In this paper, we investigate the structure of the duals of fusion frames and discuss the relation between the duals of fusion fram...

Extending and improving the concepts: woven frame and fusion frames, we introduce the notion of woven fusion frames in Hilbert spaces. We clarify our extension and generalization by some examples of woven frames and woven fusion frames. Also, we present some properties of woven fusion frames, especially we show that for given two woven frames of sequences, one can build woven fusion frames and ...

let x be a hypergroup. in this paper, we study the homomorphisms on certain subspaces of l(x)* which are weak*-weak* continuous.

The study of the c$k$-fusions frames shows that the emphasis on the measure spaces introduces a new idea, although some similar properties with the discrete case are raised. Moreover, due to the nature of measure spaces, we have to use new techniques for new results. Especially, the topic of the dual of frames  which is important for frame applications, have been specified  completely for the c...