Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Conditionally compact semitopological one-parameter inverse semigroups of partial isometries


Author: M. O. Bertman
Journal: Trans. Amer. Math. Soc. 240 (1978), 263-275
MSC: Primary 22A20; Secondary 47D05
MathSciNet review: 0476906
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The algebraic structure of one-parameter inverse semigroups has been completely described. Furthermore, if B is the bicyclic semigroup and if B is contained in any semitopological semigroup, the relative topology on B is discrete. We show that if F is an inverse semigroup generated by an element and its inverse, and F is contained in a compact semitopological semigroup, then the relative topology is discrete; in fact, if F is any one-parameter inverse semigroup contained in a compact semitopological semigroup, then the multiplication on F is jointly continuous if and only if the inversion is continuous on F, and we describe $ \bar F$ in that case. We also show that if $ \{ {J_t}\} $ is a one-parameter semigroup of bounded linear operators on a (separable) Hilbert space, then $ \{ {J_t}\} \cup \{ J_t^\ast\} $ generates a one-parameter inverse semigroup T with $ J_t^{ - 1} = J_t^\ast$ if and only if $ \{ {J_t}\} $ is a one-parameter semigroup of partial isometries, and we describe the weak operator closure of T in that case.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 22A20, 47D05

Retrieve articles in all journals with MSC: 22A20, 47D05


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1978-0476906-7
PII: S 0002-9947(1978)0476906-7
Keywords: Partial isometries, one-parameter semigroups, inverse semigroups, compact semitopological semigroups
Article copyright: © Copyright 1978 American Mathematical Society