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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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$P(\omega )/\textrm {fin}$ and projections in the Calkin algebra
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by Eric Wofsey PDF
Proc. Amer. Math. Soc. 136 (2008), 719-726 Request permission

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
  • 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
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 136 (2008), 719-726
  • MSC (2000): Primary 03E35; Secondary 46L05
  • DOI: https://doi.org/10.1090/S0002-9939-07-09093-4
  • MathSciNet review: 2358514