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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Compact multilinear transformations


Author: Nishan Krikorian
Journal: Proc. Amer. Math. Soc. 33 (1972), 373-376
MSC: Primary 46G99; Secondary 47H99
MathSciNet review: 0295076
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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 [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0295076-1
Keywords: Multilinear transformation, compact map, $ {C^r}$ map, Taylor formula, polarization identity, tensor product, projection norm, convex balanced hull
Article copyright: © Copyright 1972 American Mathematical Society