Abstract
If 0 < p < 1 andT: Lp(0,1) →E is a continuous linear operator into a topological vector space, there is an infinite-dimensional subspaceX ofL p on whichT is an isomorphism; thus there are no compact operators onL p . Results of this type are proved for general non-locally convex Orlicz spaces.
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References
L. Drewnowski and W. Orlicz,A note on modular spaces, Bull. Acad. Polon. Sci.16 (1968), 809–814.
N. J. Kalton,A note on the spaces Lp, 0 <p ≦ 1, Proc. Amer. Math. Soc,56 (1976), 199–202.
T. Kato,Perturbation theory for nullity, deficiency and other quantities of linear operators, J. Analyse Math.6 (1958), 261–322.
M. A. Krasnoseloskii and Ya. M. Rutickii,Convex Functions and Orlicz Spaces, Nordhoff, Groningen, 1961.
D. Pallaschke,The compact endomorphisms of the metric linear spaces Lϕ, Studia Math.47 (1973), 123–133.
P. Turpin,Opérateurs linéaires entre espaces d’Orlicz non localement convexes, Studia Math.46 (1973), 153–165.
P. Turpin,Convexites dans les espaces vectoriels topologiques generaux, Thèse Orsay, 1974 (Diss. Math., to appear).
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Kalton, N.J. Compact and strictly singular operators on Orlicz spaces. Israel J. Math. 26, 126–136 (1977). https://doi.org/10.1007/BF03007663
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DOI: https://doi.org/10.1007/BF03007663