Soft Frames in Soft Hilbert Spaces

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.

Automated summary

This paper introduces the concept of discrete frames on soft Hilbert spaces using soft linear operators, extending the classical notion of frames on Hilbert spaces to algebraic structures on soft sets. The results demonstrate properties of frame operators and prove the frame decomposition theorem for every element in a soft Hilbert space. This theoretical framework has potential applications in signal processing, specifically in modeling data packets for communication networks.