ON CONDITIONAL EXPECTATION OPERATORS ON L(μ,X)(1≤p≤+∞,p≠2)

Some characterizations of the conditional expectation operators on Lebesgue-Bochnerspaces L_p(μ,X)are given,where 1≤p<∞,p≠2.Also an example is given to show thatthe characterizations of the conditional expectation operators on L_p(μ,X)are differentfrom that on L_p(μ)_z Finally,a representation of the constant-preserving contractiveprojection on spaces L_p(μ,X)is got when 0相似文献   

SCHAUDER BASIS DETERMINING PROPERTIES

In this paper we introduce a new concept, called the Schauder basis determining property, which is strictly stronger than the concept of a countably determining property. This concept provides a new way to study the structure of Banach spaces, especially, the goometrical properties of Banach spaces. We show that many structural properties of Banach spaces are Schauder basis detarmining properties. These include the Banach-Saks property, the Asplund property, full convexity, the Kadec-Klee property, zeflexity, some-what refiexity, property (A)—(E), the Schur property, and the Krein-Milman property. We also give a counterexample to show that the approximation property is not a Schauder' basis determining property, but it is a countably determining property.