Abstract
We study a matrix algebra M n(U), where U is a commutative topological nuclear entire (bounded, analytic) *-algebra. We prove that M n(U) is also a topological nuclear entire (bounded, analytic) *-algebra.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
N. Krupnik and B. Silberman, “The structure of some Banach algebras fulfilling a standard identity,” Math. Nachr., 142, 175-180 (1989).
V. S. Yakovlev, “On representations of certain commutative nuclear *-algebras,” Ukr. Mat. Zh., 39, No. 2, 235-243 (1987).
Yu. M. Berezanskii, G. Lassner, and V. S. Yakovlev, “On decomposition of positive functionals on commutative nuclear *-algebras,” Ukr. Mat. Zh., 39, No. 5, 638-641 (1987).
G. Lassner, “Topological algebras of operators,” Rept. Math. Phys., 3, No. 4, 279-293 (1979).
Yu. M. Berezanskii, “Spectral projection theorem,” Usp. Mat. Nauk, 39, No. 4, 3-52 (1984).
Yu. M. Berezanskii, Self-Adjoint Operators in Spaces of Functions of Infinitely Many Variables [in Russian], Naukova Dumka, Kiev (1978).
M. A. Naimark, Normed Rings [in Russian], Nauka, Moscow (1968).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Tishchenko, S.V. On One Class of Matrix Topological *-Algebras. Ukrainian Mathematical Journal 53, 1747–1750 (2001). https://doi.org/10.1023/A:1015260314236
Issue Date:
DOI: https://doi.org/10.1023/A:1015260314236