Some Properties of Fuzzy Hilbert Spaces

摘要

In this note, we present some properties of Felbin-type fuzzy inner product spaces and fuzzy bounded linear operators on the same spaces with some operator norms. At the first, we study representation of functionals on fuzzy Hilbert spaces. We introduce the fuzzy Hilbert-adjoint operator of a bounded linear operator on a fuzzy Hilbert space and define fuzzy adjoint operator. By a counterexample, it is shown that uniqueness of fuzzy Hilbert-adjoint operator is not valid for this fuzzy setting. Also, we prove that the fuzzy Hilbert-adjoint operator has the same norm as the operator itself and it holds similarly for fuzzy adjoint operator. Finally we study the relation between the fuzzy adjoint operator and the fuzzy Hilbert-adjoint operator.