Orlicz spaces of finitely additive set functions, linear operators, and martingales

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...

Composition Operators and Multiplication Operators on Orlicz Spaces

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Finitely Additive Supermartingales Are Differences of Martingales

It is shown that any nonnegative bounded supermartingale admits a Doob-Meyer decomposition as a difference of a martingale and an adapted increasing process upon appropriate choice of a reference probability measure which may be only finitely additive. Introduction. In [Armstrong, 1983] it is shown that every bounded finitely additive supermartingale is a decreasing process with respect to some...

Composition Operators in Orlicz Spaces

Composition operators C− between Orlicz spaces L.;6;1⁄4/ generated by measurable and nonsingular transformations − from  into itself are considered. We characterize boundedness and compactness of the composition operator between Orlicz spaces in terms of properties of the mapping − , the function ' and the measure space .;6;1⁄4/. These results generalize earlier results known for L p-spaces....

Refinements of s-Orlicz Convex Functions in Normed Linear Spaces