Soft Frames in Soft Hilbert Spaces

Osmin Ferrer, Arley Sierra and José Sanabria
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Osmin Ferrer: Departamento de Matemáticas, Facultad de Educación y Ciencias, Universidad de Sucre, Carrera 28, No. 5-267, Barrio Puerta Roja, Sincelejo 700001, Colombia
Arley Sierra: Departamento de Matemáticas, Facultad de Educación y Ciencias, Universidad de Sucre, Carrera 28, No. 5-267, Barrio Puerta Roja, Sincelejo 700001, Colombia
José Sanabria: Departamento de Matemáticas, Facultad de Educación y Ciencias, Universidad de Sucre, Carrera 28, No. 5-267, Barrio Puerta Roja, Sincelejo 700001, Colombia

Mathematics, 2021, vol. 9, issue 18, 1-15

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.

Keywords: soft sets; soft inner product; soft Hilbert space; self-adjoint operator; soft frame (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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