An approach to fuzzy Hilbert spaces. (English) Zbl 1223.46068
In 1984, Katsaras, Wu and Fang defined two kinds of fuzzy norms on a linear space to construct the fuzzy vector topological structure on the space, independently [see C. Wu and J. Fang, “Fuzzy generalization of Kolmogoroff’s theorem”, Journal of Harbin Institute of Technology, No. 1, 1–7 (1984), in Chinese]. Later, a few mathematicians have introduced and discussed several notions of fuzzy norm from different points of view. By means of the notion of a fuzzy norm presented by A. K. Mirmostafaee and the authors of this paper, the authors also define a new notion of fuzzy inner product space, establish the fuzzy Cauchy-Schwarz inequality and prove a version of the parallelogram law in this setting.
Reviewer: Congxin Wu (Harbin)
MSC:
46S40 | Fuzzy functional analysis |
26E50 | Fuzzy real analysis |
46C50 | Generalizations of inner products (semi-inner products, partial inner products, etc.) |
46S50 | Functional analysis in probabilistic metric linear spaces |