Some fundamental properties of fuzzy linear relations between vector spaces

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

Linear extensions of relations between vector spaces

LetX and Y be vector spaces over the same field K. Following the terminology of Richard Arens [Pacific J. Math. 11 (1961), 9–23], a relation F of X into Y is called linear if λF (x) ⊂ F (λx) and F (x) + F (y) ⊂ F (x+ y) for all λ ∈ K \ {0} and x, y ∈ X. After improving and supplementing some former results on linear relations, we show that a relation Φ of a linearly independent subset E of X in...

Some properties of continuous linear operators in topological vector PN-spaces

The notion of a probabilistic metric  space  corresponds to thesituations when we do not know exactly the  distance.  Probabilistic Metric space was  introduced by Karl Menger. Alsina, Schweizer and Sklar gave a general definition of  probabilistic normed space based on the definition of Menger [1]. In this note we study the PN spaces which are  topological vector spaces and the open mapping an...

Some Basic Properties of Vector Sequence Spaces

SOME PROPERTIES OF FUZZY HILBERT SPACES AND NORM OF OPERATORS

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...