On linear sections of orthogonally additive operators

A. Gumenchuk; I. Krasikova; M. Popov

doi:10.30970/ms.58.1.94-102

A. Gumenchuk Department of Biological Physics and Medical Informatics, Bukovinian State Medical University
I. Krasikova Zaporizhzhya National University
M. Popov Pomeranian University in Słupsk, Słupsk

DOI: https://doi.org/10.30970/ms.58.1.94-102

Keywords: orthogonally additive operator;, narrow operator;, C-compact operator;, AM-compact operator

Abstract

Our first result asserts that, for linear regular operators acting from a Riesz space with the principal projection property to a Banach lattice with an order continuous norm, the $C$-compactness is equivalent to the $AM$-compactness. Next we prove that, under mild assumptions, every linear section of a $C$-compact orthogonally additive operator is $AM$-compact, and every linear section of a narrow orthogonally additive operator is narrow.

Author Biographies

A. Gumenchuk, Department of Biological Physics and Medical Informatics, Bukovinian State Medical University

Department of Biological Physics and Medical Informatics, Bukovinian State Medical University

I. Krasikova, Zaporizhzhya National University

Zaporizhzhya National University

M. Popov, Pomeranian University in Słupsk, Słupsk

Institute of Mathematics

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