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Proceedings of the American Mathematical Society

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

 

 

Inverse $ *$-semigroups $ *$-generated by families of isometries


Author: Wacław Szymański
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
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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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DOI: https://doi.org/10.1090/S0002-9939-1990-0982408-2
Article copyright: © Copyright 1990 American Mathematical Society