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Admissibility of Weights on Non-normed $*$-Algebras

Author(s): S. J. Bhatt; A. Inoue; H. Ogi
Journal: Trans. Amer. Math. Soc. 351 (1999), 4629-4656.
MSC (1991): Primary 46K10, 47D40
Posted: April 12, 1999
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Abstract: The notion of weights on (topological) $*$-algebras is defined and studied. The primary purpose is to define the notions of admissibility and approximate admissibility of weights, and to investigate when a weight is admissible or approximately admissible. The results obtained are applied to vector weights and tracial weight on unbounded operator algebras, as well as to weights on smooth subalgebras of a C$^*$-algebra.

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Additional Information:

S. J. Bhatt
Affiliation: Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar 388120, Gujarat, India

A. Inoue
Affiliation: Department of Applied Mathematics, Fukuoka University, Nanakuma, Jonan-ku, Fukuoka, 814-80 Japan
Email: sm010888@ssat.fukuoka-u.ac.jp

H. Ogi
Affiliation: Department of Applied Mathematics, Fukuoka University, Nanakuma, Jonan-ku, Fukuoka, 814-80 Japan
Email: sm037255@ssat.fukuoka-u.ac.jp

DOI: 10.1090/S0002-9947-99-02414-9
PII: S 0002-9947(99)02414-9
Received by editor(s): February 23, 1997
Posted: April 12, 1999
Copyright of article: Copyright 1999, American Mathematical Society

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