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Dear authors! Submission of all materials is carried out only electronically through Online Submission System in personal account. DOI: 10.46698/g6863-7709-2981-j A Krengel Type Theorem for Compact Operators Between Locally Solid Vector Lattices
Zabeti, O.
Vladikavkaz Mathematical Journal 2023. Vol. 25. Issue 3.
Abstract:
Suppose \(X\) and \(Y\) are locally solid vector lattices. A linear operator \(T:X\to Y\) is said to be \(nb\)-compact provided that there exists a zero neighborhood \(U\subseteq X\), such that \(\overline{T(U)}\) is compact in \(Y\); \(T\) is \(bb\)-compact if for each bounded set \(B\subseteq X\), \(\overline{T(B)}\) is compact. These notions are far from being equivalent, in general. In this paper, we introduce the notion of a locally solid \(AM\)-space as an extension for \(AM\)-spaces in Banach lattices. With the aid of this concept, we establish a variant of the known Krengel's theorem for different types of compact operators between locally solid vector lattices. This extends [1, Theorem 5.7] (established for compact operators between Banach lattices) to different classes of compact operators between locally solid vector lattices.
Keywords: compact operator, the Krengel theorem, locally solid \(AM\)-space
Language: English
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For citation: Zabeti, O. A Krengel Type Theorem for Compact Operators Between Locally Solid Vector Lattices, Vladikavkaz Math. J., 2023, vol. 25, no. 3, pp.76-80. DOI 10.46698/g6863-7709-2981-j ← Contents of issue |
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