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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48.

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$0\leq X^{2}\leq X$
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by Ralph Gellar PDF
Trans. Amer. Math. Soc. 173 (1972), 341-352 Request permission

Abstract:

This paper studies the structure of elements $X$ satisfying $0 \leqslant {X^2} \leqslant X$ in a Dedekind $\sigma$-complete partially ordered real linear algebra. The lollipop-shaped possible spectrum of $X$ had been described previously. Three basic example types are described, each with possible spectrum a characteristic part of the lollipop and the possibility of splitting $X$ into a sum of these types is considered. The matrix case is scrutinized. There are applications to operator theory. Contributions to the theory of convergence in partially ordered algebras are developed for technical purposes.
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 173 (1972), 341-352
  • MSC: Primary 46A40
  • DOI: https://doi.org/10.1090/S0002-9947-1972-0318833-6
  • MathSciNet review: 0318833