Related papers: Extension of frames and bases -- II

Operator-valued frames (or g-frames) are generalizations of frames and fusion frames and have been used in packets encoding, quantum computing, theory of coherent states and more. In this paper, we give a new formula for operator-valued…

We extend the theory of operator-valued frames (resp. bases), hence the theory of frames (resp. bases), for Hilbert spaces and Hilbert C*-modules, in two folds. This extension leads us to develop the theory of operator-valued frames (resp.…

We give an operator-algebraic treatment of theory of p-approximate Schuader frames which includes the theory of operator-valued frames by Kaftal, Larson, and Zhang [\textit{Trans. AMS., 2009}], G-frames by Sun [JMAA, 2006], factorable weak…

We introduce a localization concept for operator-valued frames, where the quality of localization is measured by the associated operator-valued Gram matrix belonging to some suitable Banach algebra. We prove that intrinsic localization of…

In this paper, a new notion of frames is introduced: $\ast$-operator frame as generalization of $\ast$-frames in Hilbert $C^{\ast}$-modules introduced by A. Alijani and M. A. Dehghan \cite{Ali} and we establish some results.

Multipliers have been recently introduced by P. Balazs as operators for Bessel sequences and frames in Hilbert spaces. These are operators that combine (frame-like) analysis, a multiplication with a fixed sequence (called the symbol) and…

Operator-valued frames are natural generalization of frames that have been used in quantum computing, packets encoding, etc. In this paper, we focus on developing the theory about operator-valued frames for finite Hilbert spaces. Some…

Frames on Hilbert C*-modules have been defined for unital C*-algebras by Frank and Larson and operator valued frames on a Hilbert space have been studied in arXiv.0707.3272v1.[math.FA]. Goal of the present paper is to introduce operator…

Few years ago G\u{a}vru\c{t}a gave the notions of $K$-frame and atomic system for a linear bounded operator $K$ in a Hilbert space $\mathcal{H}$ in order to decompose $\mathcal{R}(K)$, the range of $K$, with a frame-like expansion. These…

In this paper we introduce and show some new notions and results on cg-frames of Hilbert spaces. We define cg-orthonormal bases for a Hilbert space H and verify their properties and relations with cg-frames. Actually, we present that every…

We develop a natural generalization of vector-valued frame theory, we term operator-valued frame theory, using operator-algebraic methods. This extends work of the second author and D. Han which can be viewed as the multiplicity one case…

This paper is a contribution to frame theory. Frames in a Hilbert space are generalizations of orthonormal bases. In particular, Gabor frames of $L^2(\mathbb{R})$, which are made of translations and modulations of one or more windows, are…

Frame theory has been rapidly generalized and various generalizations have been developed. In this paper, we present a brief survey of the frames in Hilbert $C^{\ast}$-modules, including frames, $\ast$-frames, g-frames, $\ast$-g-frames,…

We develop elements of a general dilation theory for operator-valued measures and bounded linear maps between operator algebras that are not necessarily completely-bounded. We prove our main results by extending and generalizing some known…

The notion of g-frames for Hilbert spaces was introduced and studied by Wenchang Sun [16] as a generalization of the notion of frames. In this paper, we define computable g-frames in computable Hilbert spaces and obtain computable versions…

Frames for operators or k-frames were recently considered by Gavruta (2012) in connection with atomic systems. Also generalized frames are important frames in the Hilbert space of bounded linear operators. Fusion frames, which are a special…

Controlled frames and g-frames were considered recently as generalizations of frames in Hilbert spaces. In this paper we generalize some of the known results in frame theory to controlled g-frames. We obtain some new properties of…

In this paper, we introduce and study frame of operators in quaternionic Hilbert spaces as a generalization of g frames which in turn generalized various notions like Pseduo frames, bounded quasi-projectors and frame of subspaces (fusion…

In this paper, we introduce the concept of continuous $g-$atomic subspace for a bounded linear operator and gives several useful continuous resolution of the identity operator on a Hilbert space by implies the theory of continuous…

Introduced by Duffin and Schaefer as a part of their work on nonhamonic fourrier series in 1952, the theory of frames has undergone a very interesting evolution in recent decades following the multiplicity of work carried out in this field.…