Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

GN-Operators

Version 1 : Received: 24 June 2022 / Approved: 27 June 2022 / Online: 27 June 2022 (11:07:31 CEST)

How to cite: Ahmadi, R.; Rahimlou, G. GN-Operators. Preprints 2022, 2022060365. https://doi.org/10.20944/preprints202206.0365.v1 Ahmadi, R.; Rahimlou, G. GN-Operators. Preprints 2022, 2022060365. https://doi.org/10.20944/preprints202206.0365.v1

Abstract

In this article, rst we are going to review the concept of ordinary frames , in more general case in measure spaces, namely, gc-frames. We try to develop the use of measure space in describing frames. Then by means of the gc-frames, we shall introduce gn-operators, which we shall show that each trace class operator has a vector-valued integral representation and vice-versa.

Keywords

Hilbert space; Lebesgue integral; trace class operator; frame; measure space

Subject

Computer Science and Mathematics, Analysis

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