关于正交加法算子的线性截面

Q3 Mathematics

Matematychni Studii Pub Date : 2022-10-31 DOI:10.30970/ms.58.1.94-102

A. Gumenchuk, I. Krasikova, M. Popov

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引用次数: 0

摘要

我们的第一个结果断言，对于从具有主投影性质的Riesz空间作用到具有阶连续范数的Banach格的线性正则算子，$C$-紧性等价于$AM$-紧度。接下来我们证明，在温和的假设下，$C$-紧正交可加算子的每个线性区间都是$AM$-紧的，并且窄正交可加运算符的每个线性区段都是窄的。

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On linear sections of orthogonally additive operators

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.

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来源期刊

Matematychni Studii Mathematics-Mathematics (all)

CiteScore

1.00

自引率

0.00%

发文量

期刊介绍： Journal is devoted to research in all fields of mathematics.