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

 

Some new equivalences of Anderson's paving conjectures


Authors: Vern I. Paulsen and Mrinal Raghupathi
Journal: Proc. Amer. Math. Soc. 136 (2008), 4275-4282
MSC (2000): Primary 46L30; Secondary 47L25
Published electronically: July 22, 2008
MathSciNet review: 2431040
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Abstract: Anderson's paving conjectures are known to be equivalent to the Kadison-Singer problem. We prove some new equivalences of Anderson's conjectures that require the paving of smaller sets of matrices. We prove that if the strictly upper triangular operators are paveable, then every 0 diagonal operator is paveable. This result follows from a new paving condition for positive operators. In addition, we prove that if the upper triangular Toeplitz operators are paveable, then all Toeplitz operators are paveable.


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Additional Information

Vern I. Paulsen
Affiliation: Department of Mathematics, University of Houston, Houston, Texas 77204
Email: vern@math.uh.edu

Mrinal Raghupathi
Affiliation: Department of Mathematics, University of Houston, Houston, Texas 77204
Email: mrinal@math.uh.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09644-5
PII: S 0002-9939(08)09644-5
Received by editor(s): September 25, 2007
Published electronically: July 22, 2008
Additional Notes: This research was supported in part by NSF grant DMS-0600191. Portions of this research were begun while the first author was a guest of the American Institute of Mathematics.
Communicated by: Marius Junge
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.