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Banach and Hilbert Spaces

In: Semilinear Evolution Equations and Their Applications

Author

Listed:
  • Toka Diagana

    (University of Alabama in Huntsville, Department of Mathematical Sciences
    Howard University, Department of Mathematics
    King Fahd University of Petroleum and Minerals)

Abstract

In this chapter we present the basic material on metric, Banach, and Hilbert spaces needed in the sequel. By design, every Hilbert space is a Banach space—with the converse being untrue. Banach and Hilbert spaces play a central role in many areas and subareas of mathematical analysis as most of the spaces encountered and utilized in practical problems turn out to be either Hilbert spaces or Banach spaces.

Suggested Citation

  • Toka Diagana, 2018. "Banach and Hilbert Spaces," Springer Books, in: Semilinear Evolution Equations and Their Applications, chapter 0, pages 1-28, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-00449-1_1
    DOI: 10.1007/978-3-030-00449-1_1
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