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On Compact Sets of Compact Operators on Banach Spaces not Containing a Copy of l^1

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dc.contributor.author Akkouchi, Mohamed
dc.date.accessioned 2016-05-20T09:55:13Z
dc.date.available 2016-05-20T09:55:13Z
dc.date.issued 2010
dc.identifier.issn 0208-6204
dc.identifier.uri http://hdl.handle.net/11089/18157
dc.description.abstract F. Galaz-Fontes (Proc. AMS., 1998) has established a criterion for a subset of the space of compact linear operators from a reflexive and separable space X into a Banach space Y to be compact. F. Mayoral (Proc. AMS., 2000) has extended this criterion to the case of Banach spaces not containing a copy of l^1 . The purpose of this note is to give a new proof of the result of F. Mayoral. In our proof, we use l^∞ -spaces, a well known result of H. P. Rosenthal and L.E. Dor which characterizes the spaces without a copy of l^1 and a recent result obtained by G. Nagy in 2007 concerining compact sets in normed spaces. We point out that another proof of Mayoral’s result was given by E. Serrano, C. Pineiro and J.M. Delgado (Proc. AMS., 2006) by using a different method. pl_PL
dc.language.iso en pl_PL
dc.publisher Łódź University Press pl_PL
dc.relation.ispartofseries Acta Universitatis Lodziensis. Folia Mathematica;1
dc.rights Uznanie autorstwa-Bez utworów zależnych 3.0 Polska *
dc.rights.uri http://creativecommons.org/licenses/by-nd/3.0/pl/ *
dc.subject Compact sets of compact operators pl_PL
dc.subject precompact sets pl_PL
dc.subject Arzela-Ascoli Theorem pl_PL
dc.subject relatively compact sets in Banach spaces pl_PL
dc.subject duality pl_PL
dc.subject weak topologies pl_PL
dc.subject Banach spaces not containing a copy of l^1 pl_PL
dc.title On Compact Sets of Compact Operators on Banach Spaces not Containing a Copy of l^1 pl_PL
dc.type Article pl_PL
dc.rights.holder © 2010 for University of Łódź Press pl_PL
dc.page.number 11-16 pl_PL
dc.contributor.authorAffiliation Université Cadi Ayyad, Faculté des Sciences-Semlalia, Département de Mathéma- tiques Avenue Prince My. Abdellah, BP. 2390, Marrakech – Maroc – (Morocco) pl_PL
dc.references P.M. Anselone, Compactness properties of sets of operators and their adjoints, Math. Z. 113, (1970), pp. 233-236. pl_PL
dc.references N. Bourbaki, Topologie Générale, Tome II: Chapitres 5 à 10, Hermann, Paris, 1974. pl_PL
dc.references J. Diestel, Sequences and Series in Banach Spaces, Springer-Verlag, New-York, 1984. pl_PL
dc.references L.E. Dor, On sequences spanning a complex l^1 -space, Proc. Amer. Math. Soc. 47 (1975), pp. 515-516. pl_PL
dc.references N. Dunford and J.T. Schwartz, Linear Operators. Part I: General Theory, Wiley Inter- science, New York and London, 1958. pl_PL
dc.references F. Galaz-Fontes, Note on compact sets of compact operators on a reflexive and sepa- rable banach space, Proc. Amer. Math. Soc. 126, 2 (1998), pp. 587-588. pl_PL
dc.references F. Mayoral, Compact sets of compact operators In absence of l^1 , Proc. Amer. Math. Soc. 129, 1, (2000), pp. 79-82. pl_PL
dc.references G. Nagy, A functional analysis point of view on Arzela-Ascoli Theorem, Real Analysis Exchange 32, 2 (2007), pp. 583-586. pl_PL
dc.references T.W. Palmer, Totally bounded sets of precompact linear operators, Proc. Amer. Math. Soc. 20, (1969), pp. 101-106. pl_PL
dc.references H.P. Rosenthal, A characterization of Banach spaces containing l^1 , Proc. Nat. Acad. Sci. USA 71, 6 (1974), pp. 2411-2413. pl_PL
dc.references E. Serrano, C. Pineiro and J.M. Delgado: Equicompact sets of operators defined on Banach spaces, Proc. Amer. Math. Soc. 134 (2006), pp. 689-695. pl_PL
dc.references K. Vala, Compact set of compact operators, Ann. Acad. Sci. Fenn. Ser. A I, 351 (1964), pp. 1-9. pl_PL
dc.contributor.authorEmail akkouchimo@yahoo.fr pl_PL
dc.relation.volume 17 pl_PL

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