Premium
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.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom