Transactions of the American Mathematical Society

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.

1.: G. R. Allan, A spectral theory for locally convex algebras, Proc. London Math. Soc., 15 (1965), 399-421. MR 31:619
2.: G. R. Allan, On a class of locally convex algebras, Proc. London Math. Soc., 17 (1967), 91-114. MR 34:4937
3.: J. -P. Antoine, H. Ogi, A. Inoue and C. Trapani, Standard generalized vectors on the space of Hilbert-Schmidt operators, Ann. Inst. H. Poincaré, 63 (1995), 177-210. MR 96i:47082
4.: R. Arens, The space $L^\omega$ and convex topological rings, Bull. Amer. Math. Soc., 52 (1946), 931-935. MR 8:165d
5.: B. A. Barnes, The properties -regularity and uniqueness of C-norm in a general -algebra, Trans. Amer. Math. Soc., 279 (1983), 841-859. MR 85f:46100
6.: S. J. Bhatt, Representability of positive functionals on abstract star algebras without identity with applications to locally convex -algebras, Yokohama Math. J., 29 (1981), 7-16. MR 83d:46068
7.: F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer-Velag, Berlin, Heidelberg, New York, 1973. MR 54:11013
8.: A. F. Chamseddine, J. Fröhlich and O. Grandjean, The gravitational sector in the Connes-Lott formulation of the standard model, J. Math. Phys., 36 (1995), 6255-6275. MR 96m:81256
9.: F. Cipriani, D. Guido and S. Searlatti, A remark on trace properties of $K$ -cycles, J. Operator Theory, 35 (1996), 179-189. MR 97d:46089
10.: A. Connes, Non-commutative geometry and reality, J. Math. Phys., 36 (1995), 6194-6231. MR 96g:58014
11.: J. Dixmier, C-algebras, North Holland, 1977. MR 56:16388
12.: P. G. Dixon, Generalized B-algebras, Proc. London Math. Soc., 21 (1970), 693-715. MR 43:3811
13.: J. M. G. Fell and R. S. Doran, Representations of -Algebras, Locally Compact Groups and Banach -Algebraic Bundles, Vols. I, II, Academic Press, 1988. MR 90c:46001; MR 90c:46002
14.: S. P. Gudder and R. L. Hudson, A noncommutative probability theory, Trans. Amer. Math. Soc., 245 (1978), 1-41. MR 81m:46092
15.: A. Inoue, An unbounded generalization of the Tomita-Takezaki theory I, II, Publ. RIMS, Kyoto Univ., 22 (1986), 725-765: 23 (1987), 673-726. MR 88c:47094; MR 89d:47107
16.: A. Inoue, O-algebras in standard system, Math. Nachr., 172 (1995), 171-190. MR 96e:47050
17.: A. Inoue and W. Karwowski, Cyclic generalized vectors for algebras of unbounded operators, Publ. RIMS, Kyoto Univ., 30 (1994), 577-601. MR 96a:47081
18.: A. Inoue and H. Ogi, Regular weights on algebras of unbounded operators, J. Math. Soc. Japan, 50 (1998), 227-252. CMP 98:05
19.: T. W. Palmer, Banach Algebras and General Theory of -Algebras, Vol I, Cambridge Univ. Press, 1994. MR 95c:46002
20.: T. W. Palmer, Spectral algebras, Rocky Mountain J. Math., 22 (1992), 293-328. MR 93d:46079
21.: N. C. Phillips, Inverse limits of C-algebras, J. Operator Theory, 19 (1988), 159-195. MR 90c:46090
22.: J. D. Powell, Representations of locally convex -algebras, Proc. Amer. Math. Soc., 44 (1974), 341-346. MR 50:14248
23.: R. T. Powers, Self-adjoint algebras of unbounded operators, Commun. Math. Phys., 21 (1971), 85-124. MR 44:811
24.: C. E. Rickart, General Theory of Banach Algebras, Van Nostrand, 1960. MR 22:5903
25.: K. Schmüdgen, Unbounded Operator Algebras and Representation Theory, Akademie-Verlag, 1990. MR 91f:47062
26.: K. Takesue, Standard representations induced by positive linear functionals, Mem. Fac. Sci. Kyushu Univ., 37 (1983), 211-225. MR 85j:46096

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 46K10, 47D40

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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