THE MERCER’S THEOREM FOR PARTIAL INTEGRAL OPERATORS

Kudaybergenov K. Arziev A. Orinbaev P. Tangirbergen A.
April 2023 Springer

Journal of Mathematical Sciences (United States)
2023 #271 Issue 6 749 - 761 pp.

In this paper, we study partial integral operators in Kaplansky-Hilbert module. A modular and cyclic modular spectrum of such operators is described, and a corresponding example is given. In addition, a variant of the Mercer theorem for partial integral operators with a symmetric and positive kernel has been proved.

A ring of measurable functions , Banach-Kantorovich space , Kaplansky-Hilbert module , Mercer’s theorem , Modular spectrum , Partial integral operator

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Institute for Advances Study in Mathematics, Harbin Institute of Technologies, Harbin, 150001, China
North Caucasus Center for Mathematical Research, Vladikavkaz, 362027, Russian Federation
V.I.Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, 9 University Street, Olmazor District, Tashkent, 100174, Uzbekistan
Department of Mathematics, Karakalpak State University, 1 Ch. Abdirov, Nukus, 230112, Uzbekistan
K.Zhubanov ARU, 34 Moldagulova Prospect, Aktobe, 030000, Kazakhstan

Institute for Advances Study in Mathematics
North Caucasus Center for Mathematical Research
V.I.Romanovskiy Institute of Mathematics
Department of Mathematics
K.Zhubanov ARU

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