Soft frames in soft hilbert spaces

Abstract:

In this paper, we use soft linear operators to introduce the notion of discrete frames on soft Hilbert spaces, which extends the classical notion of frames on Hilbert spaces to the context of algebraic structures on soft sets. Among other results, we show that the frame operator associated to a soft discrete frame is bounded, self-adjoint, invertible and with a bounded inverse. Furthermore, we prove that every element in a soft Hilbert space satisfies the frame decomposition theorem. This theoretical framework is potentially applicable in signal processing because the frame coefficients serve to model the data packets to be transmitted in communication networks.

Año de publicación:

2021

Keywords:

• Self-adjoint operator
• Soft inner product
• Soft sets
• Soft frame
• Soft Hilbert space

Fuente:

scopus