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A Characterization of C ∞ ‐Smooth Banach Spaces
Author(s) -
Deville Robert
Publication year - 1990
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/22.1.13
Subject(s) - mathematics , banach space , unit sphere , subspace topology , bounded function , polynomial , characterization (materials science) , unit (ring theory) , pure mathematics , space (punctuation) , combinatorics , mathematical analysis , physics , linguistics , philosophy , mathematics education , optics
We show that if X is a Banach space, X does not contain a subspace isomorphic to c o (N) and there X a nonzero real‐valued C ∞‐smooth function with bounded support if and only if there is a polynomial on X which vanishes at the origin and with values greater than 1 on the unit sphere.
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