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Matrix Transformations and Measures of Noncompactness

In: Operators Between Sequence Spaces and Applications

Author

Listed:
  • Bruno de Malafosse

    (University of Le Havre (LMAH))

  • Eberhard Malkowsky

    (Univerzitet Union Nikola Tesla, Faculty of Management)

  • Vladimir Rakočević

    (University of Niš, Department of Mathematics)

Abstract

The major part of this chapter is introductory and included as a reference for the reader’s convenience; it recalls the concepts and results from the theories of sequence spaces, matrix transformations in Sects. 1.1–1.3, and 1.5 and measures of noncompactness in Sects. 1.7–1.10 that are absolutely essential for the book. Although the results of this chapter may be considered as standard in the modern theories of matrix transformations, we included their proofs with the exception of those in Sect. 1.4 on the relations between various kind of duals; these results are mainly included for the sake of completeness and not directly used in the remainder of the book.

Suggested Citation

  • Bruno de Malafosse & Eberhard Malkowsky & Vladimir Rakočević, 2021. "Matrix Transformations and Measures of Noncompactness," Springer Books, in: Operators Between Sequence Spaces and Applications, chapter 0, pages 1-45, Springer.
    • Handle: RePEc:spr:sprchp:978-981-15-9742-8_1
    DOI: 10.1007/978-981-15-9742-8_1
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