James' space

In the area of mathematics known as functional analysis, James' space is an important example in the theory of Banach spaces and commonly serves as useful counterexample to general statements concerning the structure of general Banach spaces. The space was first introduced in 1950 in a short paper by Robert C. James.^[1]

James' space serves as an example of a space that is isometrically isomorphic to its double dual, while not being reflexive. Furthermore, James' space has a basis, while having no unconditional basis.

^ James, Robert C. A Non-Reflexive Banach Space Isometric With Its Second Conjugate Space. Proceedings of the National Academy of Sciences of the United States of America 37, no. 3 (March 1951): 174–77.

[1] James, Robert C. A Non-Reflexive Banach Space Isometric With Its Second Conjugate Space. Proceedings of the National Academy of Sciences of the United States of America 37, no. 3 (March 1951): 174–77.

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