On positive strictly singular operators and domination

On positive strictly singular operators and domination

We study the domination problem by positive strictly singular operators between Banach lattices. Precisely we show that if E and F are two Banach lattices such that the norms on E' and F are order continuous and E satisfies the subsequence splitting property, and 0< or =S< or = T : E [Rig...

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Veröffentlicht in:Positivity (Dordrecht) 2003-06, Vol.7 (1-2), p.73-80
Hauptverfasser: FLORES, Julio, HERNANDEZ, Francisco L
Format: Artikel
Sprache:eng
Schlagworte:
Banach spaces
Exact sciences and technology
Mathematical analysis
Mathematical models
Mathematics
Operator theory
Sciences and techniques of general use
Studies
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Zusammenfassung:We study the domination problem by positive strictly singular operators between Banach lattices. Precisely we show that if E and F are two Banach lattices such that the norms on E' and F are order continuous and E satisfies the subsequence splitting property, and 0< or =S< or = T : E [Right arrow] F are two positive operators, then T strictly singular implies S strictly singular. The special case of endomorphisms is also considered. Applications to the class of %strictly co-singular (or Pelczynski) operators are given too. [PUBLICATION ABSTRACT]
ISSN:1385-1292
1572-9281
DOI:10.1023/A:1025836620741