Related papers: Results on Continuous $K$-frames for Quaternionic …
If $\left(\h,\langle\cdot,\cdot\rangle\right)$ is a Hilbert space and on it we consider the sesquilinear form $\langle\,W\cdot,\cdot\rangle$ so-called $W$-metric, where $W^{*}=W\in\BH$, and $\ker\,W=\{0\}$, then the space…
In this work, we introduce a new concept of integral $K$-operator frame for the set of all adjointable operators from Hilbert $C^{\ast}$-modules $\mathcal{H}$ to it self noted $End_{\mathcal{A}}^{\ast}(\mathcal{H}) $. We give some propertis…
The notion of a K-frame in n-Hilbert space is presented and some of their characterizations are given. We verify that sum of two K-frames is also a K-frame in n-Hilbert space. Also, the concept of tight K-frame in n-Hilbert space is…
The paper is concerned with the following question: if $A$ and $B$ are two bounded operators between Hilbert spaces $\mathcal{H}$ and $\mathcal{K}$, and $\mathcal{M}$ and $\mathcal{N}$ are two closed subspaces in $\mathcal{H}$, when will…
Frame Theory has a great revolution in recent years. This Theory have been extended from Hilbert spaces to Hilbert $C^{\ast}$-modules. In this paper we consider the stability of continuous operator frame and continuous $K$-operator frames…
In this paper, we characterize and study the concept of controlled continuous $g$-frame which is an extension of continuous $g$-frame in Hilbert spaces. We introduce the concept of controlled continuous dual $g$-frame and observe some…
Frames formed by orbits of vectors through the iteration of a bounded operator have recently attracted considerable attention, in particular due to its applications to dynamical sampling. In this article, we consider two commuting bounded…
Given a total sequence in a Hilbert space, we speak of an upper (resp. lower) semi-frame if only the upper (resp. lower) frame bound is valid. Equivalently, for an upper semi-frame, the frame operator is bounded, but has an unbounded…
We introduce the notion of weaving continuous controlled K-g-fusion frame in Hilbert space. Some characterizations of weaving continuous controlled K-g-fusion frame have been presented. We extend some of the recent results of woven…
K-frame theory was recently introduced to reconstruct elements from the range of a bounded linear operator K in a separable Hilbert space. This significant property is worthwhile especially in some problems arising in sampling theory. Some…
In this paper, we introduce the concept of semi-continuous $g$-frames in Hilbert spaces. We first construct an example of semi-continuous $g$-frames using the Fourier transform of the Heisenberg group and study the structure of such frames.…
In this paper we examine the general theory of continuous frame multipliers in Hilbert space. These operators are a generalization of the widely used notion of (discrete) frame multipliers. Well-known examples include Anti-Wick operators,…
We give a characterization of K-g-fusion frames and discuss the stability of dual g-fusion frames. We also present a necessary and sufficient condition for a quotient operator to be bounded.
In this paper, we first introduce the notion of controlled weaving K-g-frames in Hilbert spaces. Then, we present sufficient conditions for controlled weaving K-g-frames in separable Hilbert spaces. Also, a characterization of controlled…
$K$-fusion frames are a generalization of fusion frames in frame theory. In this paper, we extend the concept of controlled fusion frames to controlled $K$-fusion frames, and we develop some results on the controlled $K$-fusion frames for…
We introduce the notion of a continuous biframe in a Hilbert space which is a generalization of discrete biframe in Hilbert space. Representation theorem for this type of generalized frame is verified and some characterizations of this…
Gavruta introduced $K$-frames for Hilbert spaces to study atomic systems with respect to a bounded linear operator. There are many differences between K-frames and standard frames, so we study weaving properties of K-frames. Two frames…
We introduce the notion of continuous frame in n-Hilbert space which is a generalization of discrete frame in n-Hilbert space. The tensor product of Hilbert spaces is a very important topic in mathematics. Here we also introduce the concept…
The aim of this work is to define a continuous functional calculus in quaternionic Hilbert spaces, starting from basic issues regarding the notion of spherical spectrum of a normal operator. As properties of the spherical spectrum suggest,…
A $J$-frame for a Krein space $\mathcal{H}$ is in particular a frame for $\mathcal{H}$ (in the Hilbert space sense). But it is also compatible with the indefinite inner-product of $\mathcal{H}$, meaning that it determines a pair of maximal…