New Constructions of Scalable K-frames

Document Type : Original Article

Author
Hessam Hosseinnezhad
Department of Basic Sciences, Shahid Sattari Aeronautical University of Science and Technology, Tehran, Iran
10.22034/maco.5.2.9
Abstract
The invariance of frames and their extensions under the operator perturbation is one of the most important problems in frame theory.
In this paper, we focus on the stabilities of scalable K-frames under the operator perturbation and then
we construct new scalable K-frames for Hilbert spaces by some operator theory tools.
More precisely, we investigate several sufficient and/or conditions
of the operator perturbation for a scalable K-frame by using certain operators with specific properties.
Finally, since the finite sum of scalable K-frames may not be a scalable K-frames for
the Hilbert space, we demonstrate that under some special conditions, the sum of two scalable K-frames remains a scalable K-frame.

Keywords

Subjects

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Mathematical Analysis and Convex Optimization
Volume 5, Issue 2
December 2025