Basic Concepts in the Geometry of Banach Spaces

By William B. Johnson, J. Lindenstrauss. 2001

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Approximating the cut-norm via Grothendieck's inequality (2004, result): “We believe, however, that although the value of ρ obtained in this section is rather poor, the method, which is motivated by the proof of Grothendieck’s inequality in [7] (page 15) and in [16] (page 68) is interesting and may lead to similar results for related problems.”
An arithmetic proof of John’s ellipsoid theorem (2005, background): “For references to other proofs, a generalization and to the numerous applications see [2, 6, 8, 12].”
Dynamical entropy in Banach spaces (2004, background): “For terminology related to Banach spaces see [42, 34].”
Chapter 36 - The Banach Spaces C(K) (2003, methodology): “) Of course the relation c ↪→ is implicit in the decomposition method given on page 14 of [JL], which was developed by A.”
Separable lifting property and extensions of local reflexivity (2001, unknown): “Since C([0, 1])∗∗ is 1-injective (see [12] or [14]), j has a contractive extension j̃ : Z → C([0, 1])∗∗.”