Atomic and nonatomic Operator-Valued Measures in Locally Convex Cones
AbstractThe operator valued measures and integrals for cone-valued functions have been investigated in [W. Roth, Operator-valued measures and integrals for cone-valued functions, Lecture Notes in Mathematics, vol. 1964, 2009, Springer Verlag, Heidelberg-Berlin-New York]. In this paper, we define atomic and nonatomic operator valued measures in locally convex cones and investigate their properties. We prove that every operator valued measure can be written as the sum of an atomic and a nonatomic measures.
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