$K$-frames as a generalization of frames were introduced by L. Gu{a}vruc{t}a to study atomic systems on Hilbert spaces which allows, in a stable way, to reconstruct elements from the range of the bounded linear operator $K$ in a Hilbert space. Recently some generalizations of this concept are introduced and some of its difference with ordinary frames are studied. In this paper, we give a new ge...

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 part...

In this paper, by using the sequence of adjointable operators from pro-C*-algebra $ mathcal{A} $ into a Hilbert $ mathcal{A} $-module $ E $. We introduce frames with bounds in pro-C*-algebra $ mathcal{A} $. New frames in Hilbert modules over pro-C*-algebras are called standard $ ast $-frames of multipliers. Meanwhile, we study several useful properties of standard $ ast $-frames in Hilbert modu...

in this note‎, ‎we aim to show that several known generalizations of frames are equivalent to the continuous frame‎ ‎defined by ali et al‎. ‎in 1993‎. ‎indeed‎, ‎it is shown that these generalizations can be considered as an operator between two hilbert spaces‎.

We introduce a new g-frame (singleton g-frame), g-orthonormal basis and g-Riesz basis and study corresponding notions in some other generalizations of frames.Also, we investigate duality  for some kinds of g-frames. Finally, we illustrate an example which provides a  suitable translation from discrete frames to Sun's g-frames.

yielding elements (ye) are among those devices that not only help control structural damages, but make better seismic behavior by concentrating the frames in some removable part of the structures. ye are located at the intersection of concentric braced frame (cbf) in a rectangular shape. in this paper, seismic behavior of the frames with ye will be investigated. for this reason, 5 braced steel ...

Finite tight frames have many applications and some interesting physical interpretations. One of the important subjects in this area is the ways for constructing such frames. In this article we give a concrete method for constructing finite normalized frames using Platonic solids.