Compact multilinear transformations
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- by Nishan Krikorian PDF
- Proc. Amer. Math. Soc. 33 (1972), 373-376 Request permission
Abstract:
It is well known that if a ${C^1}$ map between Banach spaces is compact, then its derivative is a compact operator. If the map is ${C^r}$, then what can be said about the compactness of its higher derivatives? This question leads us to a study of compact multilinear operators with the main result being that the higher derivatives of a compact map are such operators.References
- J. Dieudonné, Foundations of modern analysis, Pure and Applied Mathematics, Vol. 10-I, Academic Press, New York-London, 1969. Enlarged and corrected printing. MR 0349288 S. Mazur and W. Orlicz, Grundlegende Eigenschaften der polynomischen Operationen, Studia Math. 5 (1934), 50-68.
- François Trèves, Topological vector spaces, distributions and kernels, Academic Press, New York-London, 1967. MR 0225131 M. M. Vainberg, Variational methods for the study of nonlinear operations, GITTL, Moscow, 1956; English transl., Holden-Day, San Francisco, Calif., 1964. MR 19,567; MR 31 #638.
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 33 (1972), 373-376
- MSC: Primary 46G99; Secondary 47H99
- DOI: https://doi.org/10.1090/S0002-9939-1972-0295076-1
- MathSciNet review: 0295076