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Real Interpolation and Closed Operator Ideals


Cobos, Fernando and Fernández-Cabrera, Luz M. and Manzano, Antonio and Martínez, Antón (2004) Real Interpolation and Closed Operator Ideals. Journal de Mathématiques Pures et Appliquées, 83 (3). pp. 417-432. ISSN 0021-7824

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We investigate the behaviour by general J- and K-methods of certain closed operator ideals. In particular, the results apply to weakly compact operators, Rosenthal operators and Banach–Saks operators.

Item Type:Article
Uncontrolled Keywords: Banach-Spaces; L1; Real Interpolation; Weakly Compact Operators; Rosenthal Operators; Banach-Saks Operators; Mathematics, Applied; Mathematics
Subjects:Sciences > Mathematics > Numerical analysis
ID Code:15081

B. Beauzamy, Espaces d’interpolation réels: topologie et géométrie, in: Lecture Notes in Math., vol. 666, Springer-Verlag, Berlin/New York, 1978.

C. Bennett, R. Sharpley, Interpolation of Operators, Academic Press, New York, 1988.

J. Bergh, J. Löfström, Interpolation Spaces. An Introduction, Springer-Verlag, Berlin/New York, 1976.

Y. Brudnyˇı, N. Krugljak, Interpolation Functors and Interpolation Spaces, vol. 1, North-Holland, Amsterdam, 1991.

A.P. Calderón, Spaces between L1 and L ∞ and the theorem of Marcinkiewicz, Studia Math. 26 (1966) 273–299.

F. Cobos, M. Cwikel, P. Matos, Best possible compactness results of Lions–Peetre type, Proc. Edinburgh Math. Soc. 44 (2001) 153–172.

F. Cobos, L.M. Fernández-Cabrera, A. Martínez, Compact operators between K- and J -spaces, Studia Math., in press.

F. Cobos, A. Manzano, A. Martínez, Interpolation theory and measures related to operator ideals, Quart. J. Math. 50 (1999) 401–416.

F. Cobos, A. Manzano, A. Martínez, P. Matos, On interpolation of strictly singular operators, strictly cosingular operators and related operator ideals, Proc. Roy. Soc. Edinburgh Sect. A 130 (2000) 971–989.

F. Cobos, A. Martínez, Extreme estimates for interpolated operators by the real method, J. London Math. Soc. 60 (1999) 860–870.

M. Cwikel, J. Peetre, Abstract K and J spaces, J. Math. Pures Appl. 60 (1981) 1–50.

W.J. Davis, T. Figiel, W.B. Johnson, A. Pelczy´nski, Factoring weakly compact operators, J. Funct. Anal. 17 (1974) 311–327.

J. Diestel, H. Jarchow, A. Tonge, Absolutely Summing Operators, in: Cambridge Stud. Adv. Math., vol. 43, Cambridge Univ. Press, Cambridge, UK, 1995.

P. Erd˝os, M. Magidor, A note on regular methods of summability and the Banach–Saks property, Proc. Amer. Math. Soc. 59 (1976) 232–234.

J. Gustavsson, A function parameter in connection with interpolation of Banach spaces, Math. Scand. 42 (1978) 289–305.

S. Heinrich, Closed operator ideals and interpolation, J. Funct. Anal. 35 (1980) 397–411.

S. Janson, Minimal and maximal methods of interpolation, J. Funct. Anal. 44 (1981) 50–73.

S.G. Kreˇın, Ju.I. Petunin, E.M. Semenov, Interpolation of Linear Operators, Amer. Math. Soc., Providence, RI, 1982.

G.Ya. Lozanovskii, On some Banach lattices, Siberian Math. J. 10 (1969) 419–431.

L. Maligranda, A. Quevedo, Interpolation of weakly compact operators, Arch. Math. 55 (1990) 280–284.

M. Mastylo, Interpolation spaces not containing &1, J. Math. Pures Appl. 68 (1989) 153–162.

M. Mastylo, On interpolation of weakly compact operators, Hokkaido Math. J. 22 (1993) 105–114.

B.S. Mitjagin, An interpolation theorem for modular spaces, Mat. Sbornik 66 (1965) 472–482.

P. Nilsson, Reiteration theorems for real interpolation and approximation spaces, Ann. Mat. Pura Appl. 132 (1982) 291–330.

P. Nilsson, Interpolation of Calderón and Ovchinnikov pairs, Ann. Mat. Pura Appl. 134 (1983) 201–232.

J. Peetre, A theory of interpolation of normed spaces, Notes Mat. 39 (1968) 1–86. Lecture Notes, Brasilia, 1963.

A. Pietsch, Operator Ideals, North-Holland, Amsterdam, 1980.

A. Quevedo, Some remarks on the reflexivity of the real interpolation space, J. Math. Anal. Appl. 162 (1991) 189–195.

H.P. Rosenthal, A characterization of Banach spaces containing &1, Proc. Natl. Acad. Sci. USA 71 (1974) 2411–2413.

H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam, 1978.

A.C. Zaanen, Riesz Spaces II, North-Holland, Amsterdam, 1983.

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