Research PaperFree Access

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

School of Mathematics Science, Xinjiang Normal University, Urumqi, Xinjiang 830054, P. R. China

https://doi.org/10.1142/S0219691323500352Cited by:0 (Source: Crossref)

Abstract

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

Keywords:

AMSC: 42C15, 42C40, 41A58

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