2007/02/12 by Eric Wofsey, Wofsey, Eric
Mathematics · #03E35 (Primary) 46L05 (Secondary) #Advanced Banach Space Theory #Advanced Topics in Algebra #Advanced Topology and Set Theory #FOS: Mathematics #Logic (math.LO) #Operator Algebras (math.OA) #math.LO #math.OA #msc:03E35 #msc:46L05
paper · pdf · doi:10.48550/arxiv.math/0702309
8 pages; to appear in Proceedings of the AMS
arxiv created 2007/02/12 · openalex publication_date 2007/02/12 · arxiv updated 2009/12/01 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28
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(ω)/\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(ω)/\rm fin.