ON THE STUDY OF FUZZY HILBERT SPACES BY FUZZY ISOMETRIC ISOMORPHISMS

ON THE STUDY OF FUZZY HILBERT SPACES BY FUZZY ISOMETRIC ISOMORPHISMS

B. Daraby, A. Rostami, A. Rahimi

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Abstract

In this paper, by dening a fuzzy inner product on the dual of real fuzzy Hilbert space, we show that the dual of fuzzy Hilbert space is also fuzzy Hilbert space. Then the concepts of fuzzy linear operator and fuzzy isomentric are dened. It is shown that each real fuzzy Hilbert space is isometricaly isomorphic to the dual of the fuzzy Hilbert space.

Keywords

Fuzzy Hilbert space; Fuzzy isometric; Fuzzy isomorphism; Fuzzy dual space.