A version of Kalton’s theorem for the space of regular operators

• Autores: Foivos Xanthos
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 66, Fasc. 1, 2015, págs. 55-62
• Idioma: inglés
• DOI: 10.1007/s13348-013-0101-8
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• Resumen

  • In this note we extend some recent results in the space of regular operators [appeared in Bu and Wong (Indag Math 23:199–213, 2012), Bu et al. (Collect Math 62:131–137, 2011), and Li et al. (Taiwan J Math 16:207–215, 2012)]. Our main result is the following Banach lattice version of a classical result of Kalton: Let E be an atomic Banach lattice with an order continuous norm and F a Banach lattice. Then the following are equivalent: (i) L^r(E,F) contains no copy of \ell _\infty, (ii) L^r(E,F) contains no copy of c_0, (iii) K^r(E,F) contains no copy of c_0, (iv) K^r(E,F) is a (projection) band in L^r(E,F), (v) K^r(E,F)=L^r(E,F)