Keyword: Frames In N-hilbert Space : Search

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A study on the sum of $K$ $K$ -frames in $n$ $n$ -Hilbert space
- Gang Wang
International Journal of Wavelets, Multiresolution and Information Processing01 Aug 2023
Preview 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.

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