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Further Properties of Fuzzy Banach Spaces

  • Yeol Je Cho
  • Themistocles M. Rassias
  • Reza Saadati
Chapter

Abstract

In this chapter, we consider some important properties of fuzzy Banach spaces. In Section 3.1, we discuss about finite dimensional fuzzy Banach spaces and prove some important theorems on linearly independent set. Next, we prove, in a finite dimensional vector space X, every two fuzzy norms are equivalent. Finally, we study some bounded and continuous linear operators in fuzzy normed spaces.

References

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    C. Alsina, B. Schweizer, A. Sklar, Continuity properties of probabilistic norms. J. Math. Anal. Appl. 208, 446–452 (1997)MathSciNetCrossRefGoogle Scholar
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    E. Kreyszig, Introductory Functional Analysis with Applications, Wiley Classics Library (Wiley, New York, 1989)Google Scholar
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    R.E. Megginson, An Introduction to Banach Space Theory (Springer, New York, 1998)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Yeol Je Cho
    • 1
    • 2
  • Themistocles M. Rassias
    • 3
  • Reza Saadati
    • 4
  1. 1.Department of Mathematical EducationGyeongsang National UniversityJinjuKorea (Republic of)
  2. 2.School of Mathematical ScienceUniversity of Electronic Science and Technology of ChinaChengduChina
  3. 3.Department of MathematicsNational Technical University of AthensAthensGreece
  4. 4.Department of MathematicsIran University of Science and TechnologyTehranIran

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