I'm looking for references which provide good surveys and histories of results related to Gateaux and Frechet derivatives and their relationship to Asplundness and RNP. Specifically, any papers or books which explain the underlying ideas and geometry, rather than simply proving results or leaning heavily on other unexplained existence results as a black box.
2026-04-08 07:36:56.1775633816
Frechet differentiability, RNP, and Asplundness (soft question)
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Have you read Namioka and Phelps:
Namioka, I.; Phelps, R. R., Banach spaces which are Asplund spaces, Duke Math. J. 42, 735-750 (1975). ZBL0332.46013.
In this paper the concept "Asplund space" was first proposed, and proofs of the main properties were given.