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On the length of faithful nuclear representations of finite rank operators
Author(s) -
Pełczynski A.,
Tomczak-Jaegermann Nicole
Publication year - 1988
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300006343
Subject(s) - mathematics , unit sphere , banach space , rank (graph theory) , ellipsoid , pure mathematics , isometric exercise , unit (ring theory) , mathematical analysis , combinatorics , medicine , physics , mathematics education , astronomy , physical therapy
We study the minimal length of faithful nuclear representations of operators acting between finite‐dimensional Banach spaces and the related minimal number of contact points of the John ellipsoid of maximal volume contained in the unit ball of a finite‐dimensional Banach space. In both cases the classical upper estimates, which follow from the Caratheodory theorem, are shown to be exact. Related isometric characterizations ofl n ∞are proved.