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Bochner representable operators on Köthe-Bochner spaces

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Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let E be a Banach function space and X be a real Banach space. We study Bochner representable operators from a K¨othe-Bochner space E(X) to a Banach space Y . We consider the problem of compactness and weak compactness of Bochner representable operators from E(X) (provided with the natural mixed topology) to Y .
Rocznik
Strony
113--119
Opis fizyczny
bibliogr. 23 poz.
Twórcy
autor
  • Faculty of Mathematics, Computer Science and Econometrics ul. Szafrana 4A, 65–516 Zielona Góra, Poland, M.Nowak@wmie.uz.zgora.pl
Bibliografia
  • [A1] K. Andrews, Representation of compact and weakly compact operators on the space of Bochner integrable functions, Pacific J. Math., 92, no. 2 (1981), 257-267.
  • [A2] K. Andrews, The Radon-Nikodym property for spaces of operators, J. London Math. Soc., (2), 28 (1982), 113-122.
  • [C] J.B. Cooper, Saks Spaces and Applications to Functional Analysis, North-Holland Publ. Co., Amsterdam, New York, 1978.
  • [CM] P. Cembranos and J. Mendoza, Banach spaces of vector-valued functions, Lectures Notes in Math., 1676, Springer Verlag, Berlin, Heidelberg, 1997.
  • [D] N. Dinculeanu, Vector Measures, Pergamon Press, New York, 1967.
  • [DP] , N. Dunford and J. Pettis, Linear operators on summable functions, Trans. Amer. Math. Soc., 47 (1940), 323-392.
  • [DS] N. Dunford and J. Schwartz, Linear Operators, Part. I, General Theory, Interscience, Publ. Inc., New York, 1958.
  • [DU] J. Diestel and J.J. Uhl, Vector Measures, Amer. Math. Soc., Math. Surveys 15, Providence, 1977.
  • [F] K. Feledziak, Comment. Math. Prace Mat. 37 (1997), 81-98.
  • [G1] A. Grothendieck, Sur les espaces (F) and (DF), Summa Brasil. Math. 3 (1954), 57-122.
  • [G2] A. Grothendieck, Espaces vectoriels topologiques, Sao Paulo, 1954.
  • [KA] L.V. Kantorovitch and A.V. Akilov, Functional Analysis (in Russian), Nauka Moscow, 1984 (3rd edition).
  • [L] Pei-Kee Lin, K¨othe-Bochner Function Spaces, Birkha¨user Verlag, Boston, Basel, Berlin, 2003.
  • [Na1] V.G. Navodnov, Integral representation of operators acting from a Banach space of measurable vector-valued functions into a Banach space, Izv. Vyssh. Uchebn. Zaved. Mat., no. 3 (1983), 82-84 (in Russian).
  • [Na2] V.G. Navodnov, On the theory of integral operators in spaces of measurable vector functions (Russian), Issled. Prikl. Math., 12 (1984), 162-174. Translated in J. Soviet Mat. 45, no. 2 (1989), 1093-1100.
  • [N1] M. Nowak, Mixed topology on normed function spaces, I, Bull. Polish Acad. Sci. Math., 36, no. 5-6 (1988), 251-262.
  • [N2] M. Nowak, Lebesgue topologies on vector-valued function spaces, Math. Japonica 52 no. 2 (2000), 171-182.
  • [Ph] R.S. Phillips, On linear transformations, Trans. Amer. Math. Soc. 48 (1940), 516-541.
  • [RR] M.M. Rao and Z.D. Ren, Theory of Orlicz spaces, Marcel Dekker, New York, Basel, Hong Kong, 1991.
  • [Ru] W. Ruess, [Weakly] compact operators and DF spaces, Pacific J. Math., 98, no. 2 (1982), 419-441.
  • [U1] J.J. Uhl, Compact operators on Orlicz spaces, Rend. Semin. Math. Univ. Padova 42 (1969), 209-219.
  • [U2] J.J. Uhl, On a class of operators on Orlicz spaces, Studia Math. 40 (1971), 17-22.
  • [W] A. Wiweger, Linear spaces with mixed topology, Studia Math., 20 (1961), 47-68. Marian Nowak
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS5-0019-0027
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