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 | References | Similar Articles | Additional Information

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

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.