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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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Inverse $*$-semigroups $*$-generated by families of isometries
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by Wacław Szymański PDF
Proc. Amer. Math. Soc. 108 (1990), 101-106 Request permission

Abstract:

It is shown that if a *-semigroup *-generated by a family of commuting Hilbert space isometries that commute each other, none of which commutes with the adjoint of another one, and none of which is a nonzero power of another one, consists of partial isometries, then it is singly *-generated. Also, the following result on algebraic semigroups is proved: If $S$ is an inverse *semigroup *-generated by a set $X$ satisfying the generating relations: ${a^ * }a = 1, ab = ba$, for all $a,b \in X$, then $S$ is the bicyclic semigroup. Both results follow from the special behavior of inverse *-semigroups *-generated by analytic Toeplitz operators.
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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 108 (1990), 101-106
  • MSC: Primary 47D05; Secondary 47B35
  • DOI: https://doi.org/10.1090/S0002-9939-1990-0982408-2
  • MathSciNet review: 982408