New results on K-frames

In recent years, the concepts of frame in [Formula: see text]-Hilbert space and [Formula: see text]-frames in [Formula: see text]-Hilbert space have been introduced. The [Formula: see text]-frames in the [Formula: see text]-Hilbert space are more generalized than the ordinary frames. This paper deals with the problem of sum of [Formula: see text]-frames in [Formula: see text]-Hilbert space. First, the sufficient condition for the finite sum of [Formula: see text]-frames and Bessel sequences in [Formula: see text]-Hilbert space is given. Then, some results on the operator [Formula: see text] and pre-frame operator are given, and some new results on the sum of [Formula: see text]-frame are proved. We then discuss several results for the perturbation and stability of the [Formula: see text]-frames in [Formula: see text]-Hilbert space about the sum of the [Formula: see text]-frames.

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New results on K-frames

Abstract: In this paper, we introduce some new [Formula: see text]-frames related to the adjoint of a [Formula: see text]-frame and sum of two [Formula: see text]-frames in Hilbert spaces. We prove that adjoint of a normal [Formula: see text]-frame is also a [Formula: see text]-frame.

Cited by 2 publications

References 14 publications

Tensor Product K-Dual Frames

Tensor Product K-Dual Frames

A study on the sum of K-frames in n-Hilbert space

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