$P(ω)/{\rm fin}$ and projections in the Calkin algebra

Details $P(ω)/{\rm fin}$ and projections in the Calkin algebra $P(ω)/{\rm fin}$ and projections in the Calkin algebra

2007-02-12

arxiv.org/abs/math/0702309v1

Mathematics

Logic

8 pages; to appear in Proceedings of the AMS

Scientific paper

We investigate the set-theoretic properties of the lattice of projections in the Calkin algebra of a separable infinite-dimensional Hilbert space in relation to those of the Boolean algebra $P(\omega)/{\rm fin}$, which is isomorphic to the sublattice of diagonal projections. In particular, we prove some basic consistency results about the possible cofinalities of well-ordered sequences of projections and the possible cardinalities of sets of mutually orthogonal projections that are analogous to well-known results about $P(\omega)/{\rm fin}$.

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