Doran, Robert S.2019-10-112019-10-1119801980https://repository.tcu.edu/handle/116099117/33834A systematic study of the families of projections used in the proof of Szymanski's Decomposition Theorem for Operator-valued Functions is used to generalize that result to non-hereditary properties, to sets of operators or operator-valued functions, and to sets of properties. It is demonstrated that Szymanski's conditions in fact form a characterization of the most commonly studied case of parts-decomposition results. The new results are combined with generalizations of Kubo's definition of algebraically semi-definite properties of operators to produce a simple and unified proof of a large class of parts decompositions for operator-valued functions.iv, 69 leaves, boundFormat: PrintengDecomposition (Mathematics)Von Neumann algebrasTextMain Stacks: AS38 .M663 (Regular Loan)Special Collections: AS38 .M663 (Non-Circulating)