Measures of Non-compactness of Operators on Banach Lattices

By V. G. Troitsky. 2002

51 citations recorded by the source corpus.

Abstract[Indag. Math.(N.S.)2(2) (1991), 149–158; Uspehi Mat. Nauk27(1(163)) (1972), 81–146] used representation spaces to study measures of non-compactness and spectral radii of operators on Banach lattices. In this paper, we develop representation spaces based on the nonstandard hull construction (which is equivalent to the ultrapower construction). As a particular application, we present a simple proof and some extensions of the main result of [J. Funct. Anal. 78(1) (1988), 31–55] on the monotonicity of the measure of non-compactness and the spectral radius of AM-compact operators. We also use the representation spaces to characterize d-convergence and discuss the relationship between d-convergence and the measures of non-compactness.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/dc6e52727af8a510819fc6720ad93c491ffb8bab

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In Geometry and Topology

1. M. Kandić
2. M. Marabeh
3. V. G. Troitsky
4. O. Zabeti

In Mathematical Physics

1. M. Kandić
2. M. Marabeh
3. V. G. Troitsky
4. O. Zabeti

Citations in the corpus

• Unbounded norm topology in Banach lattices (2016, background): “versity grant number BAP-01-01-2016-001. The third author was supported by an NSERC grant. 1 2 M. KANDIC, M.A.A. MARABEH, AND V.G. TROITSKY´ review of its properties. Un-convergence was introduced in [Tro04] and further investigated in [DOT]. For unexplained terminology on vector and Banach lattices”