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The Distance between a Symmetric Space and a 2‐Convex or 2‐Concave Space
Author(s) -
TomczakJaegermann Nicole
Publication year - 1981
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-24.2.272
Subject(s) - mathematics , regular polygon , combinatorics , space (punctuation) , banach space , basis (linear algebra) , constant (computer programming) , mathematical analysis , geometry , computer science , programming language , operating system
If X is a k ‐dimensional symmetric space and p is a real number with 1 ⩽ p ⩽ ∞ then the Banach‐Mazur distance d ( X ,l p k ) ⩽ c √ k , where c is a universal constant. The estimate remains valid if one replacesl p kby a k ‐dimensional space Y with unconditional basis which is either 2‐convex or 2‐concave. If both X and Y have unconditional bases and Y is either 2‐convex or 2‐concave, then d ( X, Y ) ⩽k ( 1 + log k ).