Galoitica: Journal of Mathematical Structures and Applications

“Fuzzy probability theory” appeared as a smooth extension of classical probability theory in 1995. It was expected that it will be of great importance in quantum mechanics, but the theory doesn’t keep its development as it was expected. This necessitates revising some of its fundamental basic concepts. We argue that if quantum probability theory should have less constrained than classical probability theory as can be seen in the case of joint random variables, we surely need to weaken the definition of the intersection operation. In this paper, discuss the definition validity in quantum probability theory and to discuss the consistency of the given definitions with the whole theory and the possibility to have a more suitable definition.

In this paper we generalize the concept of 2-quasi -- nuclear operators between Normed spaces to -quasi--nuclear operators between locally convex spaces and we study the relationship between p-quasi-- nuclear, nuclear operators, -nuclear, quasi-nuclear and quasi-- nuclear. Also, we prove that the composition of two operators, one of them is a -quasi--nuclear, is again a p-quasi--nuclear operator.

In this paper we give an equivalent definition of continuous and compact linear operators by using orthogonal bases in non-archimedean locally K - convex spaces. We also show that if E is a  space and F is a semi-Montel  space, then every continuous linear operator T:E→F is compact.