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Soft Frames in Soft Hilbert Spaces

Author

Listed:
  • 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)

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.

Suggested Citation

  • Osmin Ferrer & Arley Sierra & José Sanabria, 2021. "Soft Frames in Soft Hilbert Spaces," Mathematics, MDPI, vol. 9(18), pages 1-15, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:18:p:2249-:d:634872
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    References listed on IDEAS

    as
    1. Pinaki Majumdar & S. K. Samanta, 2008. "Similarity Measure Of Soft Sets," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 1-12.
    2. Zhong-Qi Xiang, 2019. "More on Inequalities for Weaving Frames in Hilbert Spaces," Mathematics, MDPI, vol. 7(2), pages 1-11, February.
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    Cited by:

    1. Osmin Ferrer & Arley Sierra & Osvaldo Polo, 2022. "Orthogonal Frames in Krein Spaces," Mathematics, MDPI, vol. 10(19), pages 1-15, October.

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