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Weak Hilbert Spaces
Author(s) -
Pisier Gilles
Publication year - 1988
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-56.3.547
Subject(s) - mathematics , pure mathematics
In recent work by V. Milman and the author, the notions of ‘weak cotype 2’ and ‘weak type 2’ Banach spaces have been implicitly introduced. We investigate here the class of Banach spaces which are both of weak cotype 2 and weak type 2, which we call ‘weak Hilbert spaces’. These spaces can be characterized in a number of ways which will be described in this paper. Our results also suggest all kinds of questions which deserve further investigation.