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Banach Spaces

In: An Introduction to Nonlinear Analysis: Theory

Author

Listed:
  • Zdzisław Denkowski

    (Jagiellonian University, Faculty of Mathematics, Physics and Computer Science Institute of Computer Science)

  • Stanisław Migórski

    (Jagiellonian University, Faculty of Mathematics, Physics and Computer Science Institute of Computer Science)

  • Nikolas S. Papageorgiou

    (National Technical University, Department of Mathematics)

Abstract

Banach space theory became a recognized part of mathematical analysis with the appearance of the book of (1932). Since then the theory had a very quick development and found many significant applications, because it is primarily concerned with infinite dimensional function spaces, which arise rather naturally in applied problems. Even the nonlinear theories developed later, exploit particular structures in Banach space theory, like Hilbert spaces or more generally reflexive and/or separable Banach spaces. So any venture into the realm of modern nonlinear analysis, demands knowledge of at least the basic aspects of Banach space theory. The purpose of this chapter is to survey those parts of the theory that will equip the reader with all the necessary tools, to deal with the nonlinear problems that follow. The treatment is by no means exhaustive. Only the very basic things are presented and the knowledgeable reader will undoubtely spot important omissions. The books mentioned in the references of this chapter, which are devoted exclusively on the theory of Banach spaces, provide a more detailed treatment of the subject and the interested reader can find there more details and additional results.

Suggested Citation

  • Zdzisław Denkowski & Stanisław Migórski & Nikolas S. Papageorgiou, 2003. "Banach Spaces," Springer Books, in: An Introduction to Nonlinear Analysis: Theory, chapter 0, pages 255-403, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4419-9158-4_3
    DOI: 10.1007/978-1-4419-9158-4_3
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