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Transactions of the American Mathematical Society

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

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Extreme points in triangular UHF algebras
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by Timothy D. Hudson, Elias G. Katsoulis and David R. Larson PDF
Trans. Amer. Math. Soc. 349 (1997), 3391-3400 Request permission

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
  • MR Author ID: 99165
  • Email: makatsov@ecuvm.cis.ecu.edu
  • David R. Larson
  • Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
  • MR Author ID: 110365
  • Email: larson@math.tamu.edu
  • 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.
  • © Copyright 1997 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 349 (1997), 3391-3400
  • MSC (1991): Primary 47D25, 46K50, 46B20
  • DOI: https://doi.org/10.1090/S0002-9947-97-01882-5
  • MathSciNet review: 1407493