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- W654091837 abstract "We say that a C*-algebra A has the `sublattice property' if the set P(A) of all projections in A is a sublattice of the projection lattice of its enveloping von Neumann algebra A**. It is shown that this property is equivalent to the requirement that all pairs of projections have strictly positive `angle'. We discuss this property in relation to some results obtained by C. Akemann and by A. Lazar. The AW* algebras with the sublattice property are characterized. We say that a C*-algebra A satisfies property L if for any representation pi, the collection oran(pi(A)) of ranges of operators in pi(A) is a lattice with respect to intersections and (non-closed) linear spans. Property L is strictly stronger than the sublattice property. We exhibit classes of algebras possessing property L. It is shown that the set of all central covers c(pi) of representations pi for which oran(pi(A)) is a lattice, is an ideal in the lattice of central projections of A**." @default.
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- W654091837 date "2005-12-30" @default.
- W654091837 modified "2023-10-07" @default.
- W654091837 title "Lattices of Projections and Operator Ranges in C*-algebras" @default.
- W654091837 hasPublicationYear "2005" @default.
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