Pokaż uproszczony rekord

dc.contributor.authorAkkouchi, Mohamed
dc.description.abstractF. 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.publisherŁódź University Presspl_PL
dc.relation.ispartofseriesActa Universitatis Lodziensis. Folia Mathematica;1
dc.rightsUznanie autorstwa-Bez utworów zależnych 3.0 Polska*
dc.subjectCompact sets of compact operatorspl_PL
dc.subjectprecompact setspl_PL
dc.subjectArzela-Ascoli Theorempl_PL
dc.subjectrelatively compact sets in Banach spacespl_PL
dc.subjectweak topologiespl_PL
dc.subjectBanach spaces not containing a copy of l^1pl_PL
dc.titleOn Compact Sets of Compact Operators on Banach Spaces not Containing a Copy of l^1pl_PL
dc.rights.holder© 2010 for University of Łódź Presspl_PL
dc.contributor.authorAffiliationUniversité Cadi Ayyad, Faculté des Sciences-Semlalia, Département de Mathéma- tiques Avenue Prince My. Abdellah, BP. 2390, Marrakech – Maroc – (Morocco)pl_PL
dc.referencesP.M. Anselone, Compactness properties of sets of operators and their adjoints, Math. Z. 113, (1970), pp. 233-236.pl_PL
dc.referencesN. Bourbaki, Topologie Générale, Tome II: Chapitres 5 à 10, Hermann, Paris, 1974.pl_PL
dc.referencesJ. Diestel, Sequences and Series in Banach Spaces, Springer-Verlag, New-York, 1984.pl_PL
dc.referencesL.E. Dor, On sequences spanning a complex l^1 -space, Proc. Amer. Math. Soc. 47 (1975), pp. 515-516.pl_PL
dc.referencesN. Dunford and J.T. Schwartz, Linear Operators. Part I: General Theory, Wiley Inter- science, New York and London, 1958.pl_PL
dc.referencesF. 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.referencesF. Mayoral, Compact sets of compact operators In absence of l^1 , Proc. Amer. Math. Soc. 129, 1, (2000), pp. 79-82.pl_PL
dc.referencesG. Nagy, A functional analysis point of view on Arzela-Ascoli Theorem, Real Analysis Exchange 32, 2 (2007), pp. 583-586.pl_PL
dc.referencesT.W. Palmer, Totally bounded sets of precompact linear operators, Proc. Amer. Math. Soc. 20, (1969), pp. 101-106.pl_PL
dc.referencesH.P. Rosenthal, A characterization of Banach spaces containing l^1 , Proc. Nat. Acad. Sci. USA 71, 6 (1974), pp. 2411-2413.pl_PL
dc.referencesE. 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.referencesK. Vala, Compact set of compact operators, Ann. Acad. Sci. Fenn. Ser. A I, 351 (1964), pp. 1-9.pl_PL

Pliki tej pozycji


Pozycja umieszczona jest w następujących kolekcjach

Pokaż uproszczony rekord

Uznanie autorstwa-Bez utworów zależnych 3.0 Polska
Poza zaznaczonymi wyjątkami, licencja tej pozycji opisana jest jako Uznanie autorstwa-Bez utworów zależnych 3.0 Polska