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Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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An application of the Moore-Penrose inverse to antisymmetric relations
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by Robert E. Hartwig PDF
Proc. Amer. Math. Soc. 78 (1980), 181-186 Request permission

Abstract:

Let R be a star-ring and let ${R_\dagger }$ denote the set of star-regular elements in R. It is shown that the relation $a\Delta b$, defined by $a{a^\ast }a = a{b^\ast }a$, is antisymmetric on ${R_\dagger }$ provided that the two-term star-cancellation law and the positive-semidefinite axiom hold in R. This includes the star-regular elements of all ${C^\ast }$-algebras, and in particular those elements in ${{\mathbf {C}}_{n \times n}}$ and $B(H)$, the bounded linear transformations on Hilbert space H.
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 78 (1980), 181-186
  • MSC: Primary 16A28; Secondary 15A09
  • DOI: https://doi.org/10.1090/S0002-9939-1980-0550489-X
  • MathSciNet review: 550489