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Yakovlev, V. S.

Representations of certain *-algebras of smooth functions. (English) Zbl 0648.46050

Ukr. Math. J. 39, No. 3, 317-319 (1987).
Translation from Ukr. Mat. Zh. 39, No.3, 400-403 (1987; Zbl 0631.46050).

MSC:

46J25 Representations of commutative topological algebras
46K10 Representations of topological algebras with involution

Keywords:

irreducible strongly continuous *-representation; algebras of smooth functions; decompositions

Citations:

Zbl 0631.46050
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Full Text: DOI

References:

[1] V. S. Yakovlev, ?On representations of certain commutative nuclear*-algebras,? Ukr. Mat. Zh.,39, No. 2, 235-243 (1987). · Zbl 0645.47040 · doi:10.1007/BF01057505
[2] I. M. Gel’fand and N. Ya. Vilenkin, Some Applications of Harmonic Analysis. Equipped Hubert Spaces [in Russian], Fizmatgiz, Moscow (1961).
[3] R. T. Powers, ?Self-adjoint algebras of unbounded operators,? Commun. Math. Phys.,21, 85-124 (1971). · Zbl 0214.14102 · doi:10.1007/BF01646746
[4] T. Husain and S. A. Warsi, ?Positive functionals on BP*-algebras,? Periodica Math. Hung.,8, No. 1, 15-28 (1977). · Zbl 0354.46034 · doi:10.1007/BF02018042
[5] Yu. M. Berezanskii, Self-Adjoint Operators in Spaces of Functions of an Infinite Number of Variables [in Russian], Naukova Dumka, Kiev (1978).
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