Abstract
LetL(X, Y) be the Banach space of all continuous linear operators fromX toY, and letK(X, Y) be the subspace of compact operators. Some versions of the classical Pitt theorem (ifp>q, thenK(l p, lq)=L(lp, lq)) for subspaces of Lorentz and Orlicz sequence spaces are established.
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References
J. Lindenstrauss and L. Tzafriri,Classical Banach Spaces, I.Sequence Spaces, Springer, Berlin-Heidelberg-New York, (1977).
E. Lacey,The Isometric Theory of Classical Banach Spaces, Springer, Berlin-Heidelberg-New York, (1974).
E. Oja, “On M-ideals of compact operators and Lorentz sequence spaces,”Proc. Estonian Acad. Sci. Phys. Math.,40, No. 1, 31–36 (1991).
A. E. Tong and D. R. Wilken, “The uncomplemented subspaceK(E, F),”Studia, Math.,37, No. 3, 227–236 (1971).
N. J. Kalton, “Spaces of compact operators,”Math. Ann.,208, No. 4, 267–278 (1974).
J. Diestel and J. J. Uhl, Jr.,Vector Measures, Amer. Math. Soc. Providence, R.I. (1977).
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Translated fromMatematicheskie Zametki, Vol. 61, No. 1, pp. 18–25, January, 1997.
Translated by V. N. Dubrovsky
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Ausekle, J.A., Oja, E.F. Pitt's theorem for the Lorentz and Orlicz sequence spaces. Math Notes 61, 16–21 (1997). https://doi.org/10.1007/BF02355003
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DOI: https://doi.org/10.1007/BF02355003