Abstract
We propose the description of the operators and isomorphisms of the spaceC[a, b] commuting with the operator of multiplication by a continuous strictly piecewise monotone function.
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References
A. H. Nasr, “The commutant of a multiplication operation,”J. Math. Phys.,23, No. 12, 2268–2270 (1982).
N. I. Berezovskii and S. S. Linchuk,Description of Invertible Elements of the Commutant of the Multiplication Operator in the Space of Square-Summable Functions [in Russian], Deposited at the Ukrainian Institute of Scientific Information, No. 207-Uk91, Chernovtsy (1991).
N. I. Beresovskii and S. S. Linchuk, “On the commutant of a multiplication operator and conditions of invertibility of its elements,”Ukr. Mat. Zh.,45, No. 1, 21–25 (1982).
M. A. Naimark,Normed Rings [in Russian], Gostekhteoretizdat, Moscow (1956).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 3, pp. 414–418, March, 1995.
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Berezovskii, M.I., Linchuk, S.S. Description of the operators and isomorphisms of the space of continuous functions commuting with the operator of multiplication. Ukr Math J 47, 481–486 (1995). https://doi.org/10.1007/BF01056312
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DOI: https://doi.org/10.1007/BF01056312