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Approximate Isometries on Finite‐Dimensional Normed Spaces
Author(s) -
Dilworth S. J.
Publication year - 1999
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/s0024609398005591
Subject(s) - mathematics , isometry (riemannian geometry) , banach space , smoothness , dimension (graph theory) , pure mathematics , mathematics subject classification , lp space , mathematical analysis
Every ε‐isometry between real normed spaces of the same finite dimension which maps the origin to the origin may be uniformly approximated to within 2ε by a linear isometry. Under a smoothness hypothesis, necessary and sufficient conditions are obtained for the same conclusion to hold for a given ε‐isometry between infinite‐dimensional Banach spaces. 1991 Mathematics Subject Classification 46B04.