gholamreza rahimlou

In this article, first we are going to review the concept of ordinary frames , in more general case in measure spaces, namely, gcframes. We try to develop the use of measure space in describing frames. Then by means of the gc-frames, we shall introduce gn-operators, which we shall show that each trace class operator has a vector-valued integral representation and vice-versa

Controlled frames in Hilbert spaces have been recently introduced by P. Balazs and etc. for improving the numerical efficiency of interactive algorithms for inverting the frame operator. In this paper we develop a theory based on g-fusion frames on Hilbert spaces, which provides exactly the frameworks not only to model new frames on Hilbert spaces but also for deriving robust operators. In particular, we can define analysis, synthesis and frame operators with representation space compatible for (C,C')-Controlled g-fusion frames, which even yield a reconstruction formula. Also, some useful concepts such as Q-dual and perturbation are introduced and investigated.

Regarding the applications of the fusion frames and generalization of them in data proceeding, their iterative is of particular importance when one of their members is deleted. In this note, a method for reconstruction of continuous generalized  usion frames and the error operator with its upper bound are presented. Also, the approximation operator for these frames will be introduced.

In this paper, we will introduce and study “Continuous weaving K-frames in Hilbert spaces”.We first introduce a useful result for the production of these frames and then examine them under the influence of a boundary operator.Due to the basic and useful use of different types of frames in restoring some deleted information in data transfer issues, we have dedicated the end of the paper to the conditions of setting the frame under the removal of some members of the measure space and we will see that, this is related to the discrete K-frames.

The notion of $k$-frames was recently introduced by Gu avruc ta in Hilbert  spaces to study atomic systems with respect to a bounded linear operator. A continuous frame is a family of vectors in a Hilbert space which allows reproductions of arbitrary elements by continuous super positions. In this manuscript, we construct a continuous $k$-frame, so called c$k$-frame along with an atomic system for this version of frames. Also we introduce a new method for obtaining the dual of a c$k$-frame and prove some new results about it.

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 Gbreve{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 and standard frames. K-frames, which are a generalization of frames, allow us in a stable way, to reconstruct elements from the range of a bounded linear operator in a Hilbert space. In this paper, we get some new results on the continuous K-frames or briefly cK-frames, namely some operators preserving and some identities for cK-frames. Also, the stability of these frames are discussed.