*-Frames for operators on Hilbert modules

TL;DR

This paper introduces *-K-frames as a new generalization of K-frames on Hilbert modules, exploring their properties, constructions, and stability under perturbations.

Contribution

The paper defines *-K-frames, studies their properties, and investigates their behavior under direct sums, tensor products, and perturbations, extending the theory of frames in Hilbert modules.

Findings

Characterization of *-K-frames

Behavior of *-K-frames under direct sum and tensor product

Perturbation stability results for *-K-frames

Abstract

K-frames were introduced by L. Gavruta to study atomic systems on Hilbert spaces. Recently some generalizations of this concept are introduced and some of its difference with ordinary frames are studied. In this paper *-K-frames are introduced and some properties of this generalization of K-frames are studied. After proving some characterizations of *-K-frames, direct sum and tensor product of *-K-frames are considered and finally some perturbation results are established.