In this paper, we first discuss about canonical dual of g<span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font...

Fusion frames have become a major tool in the implementation of distributed systems. The effectiveness of fusion frame applications in distributed systems is reflected in the efficiency of the end fusion process. This in turn is reflected in the efficiency of the inversion of the fusion frame operator SW , which in turn is heavily dependent on the sparsity of SW . We will show that sparsity of ...

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...

in this work‎, ‎an iterative method based on a matrix form of lsqr algorithm is constructed for solving the linear operator equation $mathcal{a}(x)=b$‎ ‎and the minimum frobenius norm residual problem $||mathcal{a}(x)-b||_f$‎ ‎where $xin mathcal{s}:={xin textsf{r}^{ntimes n}~|~x=mathcal{g}(x)}$‎, ‎$mathcal{f}$ is the linear operator from $textsf{r}^{ntimes n}$ onto $textsf{r}^{rtimes s}$‎, ‎$ma...

‎In this paper‎, ‎first we develop the duality concept for $g$-Bessel sequences‎ ‎and Bessel fusion sequences in Hilbert spaces‎. ‎We obtain some results about dual‎, ‎pseudo-dual ‎and approximate dual of frames and fusion frames‎. ‎We also expand every $g$-Bessel ‎sequence to a frame by summing some elements‎. ‎We define the restricted isometry property for ‎$g$-frames and generalize some resu...

1.2. Primer on Connections. Recall from Peng’s talk that a connection on P → X can be thought of in three ways: (1) As a field of horizontal subspaces: TpP = HpP⊕VpP , where V P = ker (π∗). (Note that Vp ∼= g, and Hp ∼= Tπ(p)X). (2) As a g-valued 1-form A ∈ ΩX (g) which is invariant w.r.t. the induced G-action on ΩX (g). (3) Given a representation of G on W , as a vector bundle connection on th...

In this paper, we study frames for bounded linear operators and defined the notion of Ad-operator frame for Banach spaces. A necessary and sufficient condition for a sequence of bounded linear operators to be an Ad-operator frame has been given. Some characterizations of Ad-operator frames have been discussed. Further, a method has been given to generate a -Banach frame using a Schauder frame. ...

In this chapter we survey several recent results on the existence of frames with prescribed norms and frame operator. These results are equivalent to Schur-Horn type theorems which describe possible diagonals of positive self-adjoint operators with specified spectral properties. The first infinite dimensional result of this type is due to Kadison who characterized diagonals of orthogonal projec...