Foreword
Published online by Cambridge University Press: 19 March 2010
Summary
As I believe is well known, I did not anticipate the wealth of mathematics that has resulted from the introduction of the spaces J and JT. In fact, the discovery of J was somewhat accidental. I had proved that a Banach space X is reflexive if each linear functional attains its supremum on the unit ball for any equivalent norm and if X has a basis with certain properties. This theorem lost interest when Victor Klee proved it without any assumption about a basis (Klee's theorem lost interest when I proved it with only the assumption that each linear functional attains its supremum on the given unit ball of X, but this theorem did not come easily!). However, the use of properties that had been assumed for the basis led to the realization that X** could be described explicitly if X has a basis with a certain property (later called shrinking by M.M. Day). The definition of the space J isomorphic to J** then came very easily. At a research conference about 24 years later, Charles Stegall asked what I thought about the conjecture that X ** has a subspace isomorphic with l1 if X is separable and X** is not separable. He had asked this question the year before, but I had no ideas at that time. But this time I had been working on some other things that made the idea for JT come rather easily.
One always feels great pleasure when others discover applications of something one has done.
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- The James Forest , pp. ixPublisher: Cambridge University PressPrint publication year: 1997