in the present paper we define the notion of fuzzy inner productand study the properties of the corresponding fuzzy norm. in particular, it isshown that the cauchy-schwarz inequality holds. moreover, it is proved thatevery such fuzzy inner product space can be imbedded in a complete one andthat every subspace of a fuzzy hilbert space has a complementary subspace.finally, the notions of fuzzy bo...

library standardization is mainly concerned with technical services, space and equipments, and information content of library collection with little or no regards to the user. given every country's certain social, economical and cultural conditions, specialized libraries should engage increasingly in developing information literate users on the basis of standards, rather than standardizing tech...

‎it is well known that every (real or complex) normed linear space $l$ is isometrically embeddable into $c(x)$ for some compact hausdorff space $x$‎. ‎here $x$ is the closed unit ball of $l^*$ (the set of all continuous scalar-valued linear mappings on $l$) endowed with the weak$^*$ topology‎, ‎which is compact by the banach--alaoglu theorem‎. ‎we prove that the compact hausdorff space $x$ can ...

‎In this paper‎, ‎we characterize the class of orthogonality preserving operators on an infinite-dimensional Hilbert space $H$ as scalar multiples of unitary operators between $H$ and some closed subspaces of $H$‎. ‎We show that any circle (centered at the origin) is the spectrum of an orthogonality preserving operator‎. ‎Also‎, ‎we prove that every compact normal operator is a strongly orthogo...

A norm ‖ · ‖ on R is said to be absolute if ‖(x, y)‖ = ‖(|x|, |y|)‖ for all (x, y) ∈R, and normalized if ‖(, )‖ = ‖(, )‖ = . The set of all absolute normalized norms onR is denoted by AN. Bonsall and Duncan [] showed the following characterization of absolute normalized norms on R. Namely, the set AN of all absolute normalized norms on R is in a one-to-one correspondence with the s...

in this paper, we propose a new definition of intuitionistic fuzzyquasi-metric and pseudo-metric spaces based on intuitionistic fuzzy points. weprove some properties of intuitionistic fuzzy quasi- metric and pseudo-metricspaces, and show that every intuitionistic fuzzy pseudo-metric space is intuitionisticfuzzy regular and intuitionistic fuzzy completely normal and henceintuitionistic fuzzy nor...