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.
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References
C. Alsina, B. Schweizer, A. Sklar, Continuity properties of probabilistic norms. J. Math. Anal. Appl. 208, 446–452 (1997)
E. Kreyszig, Introductory Functional Analysis with Applications, Wiley Classics Library (Wiley, New York, 1989)
R.E. Megginson, An Introduction to Banach Space Theory (Springer, New York, 1998)
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Cho, Y.J., Rassias, T.M., Saadati, R. (2018). Further Properties of Fuzzy Banach Spaces. In: Fuzzy Operator Theory in Mathematical Analysis. Springer, Cham. https://doi.org/10.1007/978-3-319-93501-0_3
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DOI: https://doi.org/10.1007/978-3-319-93501-0_3
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-93499-0
Online ISBN: 978-3-319-93501-0
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