Usually, when studying the applications and results of a theory, it becomes clear why it was interesting to define it in a certain way. However, I'm currently beginning my studies in functional analysis. I see $l^p$ spaces as a generalization of Euclidean space, for vectors in an infinitely-dimensional space. But I would like to understand the construction of this space in a logical manner, comprehending the chronology of definitions, where it originated, who defined it, and everything else. Does anyone have a good recommendation for a history on this?

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    $\begingroup$ History is messy and chronology is rarely logical or explanatory. Hilbert defined infinite dot product in connection with integral equations, but did not consider spaces with it. Schmidt defined what we now call $l^2$ in 1907 to study infinite systems of linear equations. Then Riesz went from $2$ to $p$ around 1910 simply because Schmidt's theory could be generalized (he considered even more general $L^p$). You can read details in Dieudonne's History of Functional Analysis, VI.1. $\endgroup$
    – Conifold
    Oct 22, 2023 at 8:55

1 Answer 1


As I recall, there are extensive historical notes in both:

Dunford & Schwartz, Linear Operators (Interscience, 1958)

M. M. Day, Normed Linear Spaces (Springer, 1958)


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