In this paper,we apply function parameters,introduced by Persson,to real interpolation of Lorentz martingale spaces.Some new interpolation theorems concerning Lorentz martingale spaces are formulated.The results that we obtain generalize some fundamental interpolation theorems in classical martingale Hp theory.
For a non-degenerate pair of compact quantum groups, we first construct the quantum double as an algebraic compact quantum group in an algebraic framework. Then by adopting some completion procedure, we give the universal and reduced quantum double constructions in the correspondence C*-algebraic settings, which generalize Drinfeld's quantum double construction and yield new C*-algebraic compact quantum groups.
We first prove various kinds of expressions for modulus of random convexity by using an L^0(F,R)-valued function's intermediate value theorem and the well known Hahn-Banach theorem for almost surely bounded random linear functionals, then establish some basic properties including continuity for modulus of random convexity. In particular, we express the modulus of random convexity of a special random normed module L^0(F,X)derived from a normed space X by the classical modulus of convexity of X.
