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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Extreme points in triangular UHF algebras


Authors: Timothy D. Hudson, Elias G. Katsoulis and David R. Larson
Journal: Trans. Amer. Math. Soc. 349 (1997), 3391-3400
MSC (1991): Primary 47D25, 46K50, 46B20
MathSciNet review: 1407493
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Abstract: We examine the strongly extreme point structure of the unit balls of triangular UHF algebras. The semisimple triangular UHF algebras are characterized as those for which this structure is minimal in the sense that every strongly extreme point belongs to the diagonal. In contrast to this, for the class of full nest algebras we prove a Krein-Milman type theorem which asserts that every operator in the open unit ball of the algebra is a convex combination of strongly extreme points.


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Additional Information

Timothy D. Hudson
Affiliation: Department of Mathematics, East Carolina University, Greenville, North Carolina 27858-4353
Email: tdh@.math.ecu.edu

Elias G. Katsoulis
Affiliation: Department of Mathematics, East Carolina University, Greenville, North Carolina 27858-4353
Email: makatsov@ecuvm.cis.ecu.edu

David R. Larson
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
Email: larson@math.tamu.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-97-01882-5
PII: S 0002-9947(97)01882-5
Keywords: Triangular operator algebra, strongly extreme point, UHF algebra, semisimple
Received by editor(s): January 11, 1996
Received by editor(s) in revised form: March 28, 1996
Additional Notes: The first author’s research was partially supported by NSF grant #DMS-9500566 and the Linear Analysis and Probability Workshop at Texas A&M University.
The second author’s research was partially supported by a YI grant from the Linear Analysis and Probability Workshop at Texas A&M University and a grant from East Carolina University.
The third author’s research was partially supported by NSF grant #DMS-9401544.
Article copyright: © Copyright 1997 American Mathematical Society