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 | References | Similar Articles | Additional Information

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 , 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 .

**[1]**J. Conway,*A Course in Functional Analysis*, Springer, 1994.**[2]**Don Hadwin,*Maximal nests in the Calkin algebra*, Proc. Amer. Math. Soc.**126**(1998), no. 4, 1109–1113. MR**1443829**, 10.1090/S0002-9939-98-04233-6**[3]**Stephen H. Hechler,*Short complete nested sequences in 𝛽𝑁\𝑁 and small maximal almost-disjoint families*, General Topology and Appl.**2**(1972), 139–149. MR**0307913****[4]**K. Kunen,*Set Theory: An Introduction to Independence Proofs*, North-Holland, 1980.**[5]**N. Weaver, Set Theory and C-algebras,*Bull. Symb. Logic*, to appear.

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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

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.