Hilbert–Schmidt Frames for Operators on Hilbert Spaces, By Farkhondeh Takhteh

Research

Title	Hilbert–Schmidt Frames for Operators on Hilbert Spaces
Type	Article
Keywords	Frame, K-frame, Hilbert–Schmidt frame, Hilbert–Schmidt K-frame, Hilbert–Schmidt K-atomic system
Journal	Iranian Journal of Science and Technology Transaction A-Science
DOI	10.1007/s40995-023-01527-2
Researchers	Farkhondeh Takhteh (First researcher) , Morteza Mirzaee Azandaryani (Second researcher)

Abstract

In this paper, we introduce Hilbert–Schmidt K-frames and Hilbert–Schmidt K-atomic systems, where K is a bounded operator on a Hilbert space, and we study the relationship between these two concepts. Also, Hilbert–Schmidt K-duals are defined and some of their properties are obtained, especially, we get the general form of the Hilbert–Schmidt K-duals for a given Hilbert–Schmidt K-frame. Moreover, some methods to construct Hilbert–Schmidt K-frames are presented and the stability of Hilbert Schmidt K-frames is considered.