Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



$ {}\sp \ast$-representations of the trace-class of an $ H\sp *$-algebra

Author: Lajos Molnár
Journal: Proc. Amer. Math. Soc. 115 (1992), 167-170
MSC: Primary 46K15
MathSciNet review: 1110549
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The aim of this note is to characterize the cyclic and the irreducible $ ^*$-representations of the trace-class of a proper $ {{\text{H}}^*}$-algebra.

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

  • [1] W. Ambrose, Structure theorems for a special class of Banach algebras, Trans. Amer. Math. Soc. 57 (1945), 364-386. MR 0013235 (7:126c)
  • [2] F. F. Bonsall and J.Duncan, Complete normed algebras, Springer, New York, 1973. MR 0423029 (54:11013)
  • [3] C. E. Rickart, General theory of Banach algebras, Van Nostrand, Princeton, NJ, 1960. MR 0115101 (22:5903)
  • [4] Z. Sebestyén, On representability of linear functional on $ ^*$-algebras, Period. Math. Hungar. 15 (1984), 233-239. MR 756188 (86a:46068)
  • [5] P. P. Saworotnow, Trace-class and centralizers of an $ {H^*}$-algebra, Proc. Amer. Math. Soc. 26 (1970), 101-104. MR 0267403 (42:2305)
  • [6] P. P. Saworotnow and J. C. Friedell, Trace-class for an arbitrary $ {H^*}$-algebra, Proc. Amer. Math. Soc. 26 (1970), 95-100. MR 0267402 (42:2304)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46K15

Retrieve articles in all journals with MSC: 46K15

Additional Information

Keywords: Proper $ {{\text{H}}^*}$-algebra, trace class, representable positive linear functional, cyclic and irreducible representation
Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society