Related papers: Hilbert-Schauder Frame Operators
We develope a local theory for frames on finite dimensional Hilbert spaces. In particular, a bounded frame on a finite dimensional Hilbert space contains a subset which is a good Riesz basis for a percentage (arbitrarily close to one) of…
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…
Frames in a separable quaternionic Hilbert space were introduced and studied in [17] to have more applications. In this paper, we extend the study of frames in quaternionic Hilbert spaces and introduce different types of duals of a frame in…
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…
In this paper we study some basic properties of bicomplex linear operators on bicomplex Hilbert spaces. Further we discuss some applications of Hahn-Banach theorem on bicomplex Banach modules. We also introduce and discuss some bicomplex…
Motivated by a general dilation theory for operator-valued measures, framings and bounded linear maps on operator algebras, we consider the dilation theory of the above objects with special structures. We show that every operator-valued…
We introduce the notions of L(H)-valued norms and Banach spaces with respect to L(H)-valued norms. In particular, we introduce Hilbert spaces with respect to L(H)-valued inner products. In addition, we provide several fundamental examples…
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,…
Recent research has shown that the properties of overcomplete Gabor frames and frames arising from shift-invariant systems form a precise match with certain conditions that are necessary for a frame in $L^2(\mathbf R)$ to have a…
Weaving Hilbert space frames have been introduced recently by Bemrose et al. to deal with some problems in distributed signal processing. In this paper, we survey this topic from the viewpoint of the duality principle, so we obtain new…
We give orthonormal characterizations of collectively compact (limited) sets of linear operators from a Hilbert space to a Banach space.
In this paper, we will introduce the concept of biframes for Hilbert $ C^{\ast}- $modules produced by a pair of sequences, and we present various examples of biframes. Then, we examine the characteristics of biframes from the viewpoint of…
In topological equivalence, a bounded linear operator between Banach spaces - we focus on the case of Hilbert spaces - is viewed as only acting linearly and continuously between them qua different spaces with the structure of linear…
We study the notion of recurrence and some of its variations for linear operators acting on Banach spaces. We characterize recurrence for several classes of linear operators such as weighted shifts, composition operators and multiplication…
In this paper, we introduce and study the frames in separable quaternionic Hilbert spaces. Results on the existence of frames in quaternionic Hilbert spaces have been given. Also, a characterization of frame in quaternionic Hilbert spaces…
Our main theorem is in the generality of the axioms of Hilbert space, and the theory of unbounded operators. Consider two Hilbert spaces such that their intersection contains a fixed vector space D. It is of interest to make a precise…
Frames have been investigated frequently over the last few decades due to their valuable properties, which are desirable for various applications as well as interesting for theory. Some applications additionally require distributed…
Operator-valued frame ($G$-frame), as a generalization of frame is introduced by Kaftal, Larson, and Zhang in \textit{Trans. Amer. Math. Soc.}, 361(12):6349-6385, 2009 and by Sun in \textit{J. Math. Anal. Appl.}, 322(1):437-452, 2006. It…
The notions of column and row operator space were extended by A. Lambert from Hilbert spaces to general Banach spaces. In this paper, we use column and row spaces over quotients of subspaces of general $L_p$-spaces to equip several Banach…
In the literature, frames generated by unitary representations of groups (known as group-frames) are studied only for Hilbert spaces. We make first study of frames for Banach spaces generated by isometric invertible representations of…