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Boundedness of Multiplicative Linear Functionals

Published online by Cambridge University Press:  20 November 2018

T. Husain  and
S. B. Ng
T. Husain
Affiliation:
Mcmaster University
S. B. Ng
Affiliation:
University of British Columbia
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Let A be a complex sequentially complete commutative locally m-convex topological algebra which is symmetric with continuous involution. The purpose of this note is to prove that every multiplicative linear functional on A is bounded (Theorem 3). In fact, we prove a more general result for operators on real algebras (Theorem 1) from which we derive the above result.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 2 , 01 June 1974 , pp. 213 - 215
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Michael, E. A.: Locally multiplicatively-convex topological algebras, Amer. Math. Soc. Memoirs No. 11, 1952.Google Scholar
2. Do-Sin Sya: On semi-normed rings with involutions, Izv. Akad. Nauk SSSR Ser. Mat. 23 (1959), 509-528.Google Scholar