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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Author: Eric Wofsey
Journal: Proc. Amer. Math. Soc. 136 (2008), 719-726
MSC (2000): Primary 03E35; Secondary 46L05
Published electronically: November 6, 2007
MathSciNet review: 2358514
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Abstract: 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)/\operatorname{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)/\operatorname{fin}$.


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Additional Information

Eric Wofsey
Affiliation: Department of Mathematics, Washington University in Saint Louis, Saint Louis, Missouri 63130
Email: erwofsey@artsci.wustl.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-07-09093-4
PII: S 0002-9939(07)09093-4
Received by editor(s): September 26, 2006
Received by editor(s) in revised form: December 28, 2006
Published electronically: November 6, 2007
Communicated by: Julia Knight
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.