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Why is it called Pitt's theorem? I couldn't locate the origin of the statement.

user66081
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In the book Topics in Banach space theory. F. Albiac, N. Kalton on the page 31 it is said that the originall paper is A Note on Bilinear Forms J. London Math. Soc. (1936) s1-11 (3): 174-180.

Norbert
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  • They didn't use to have very informative titles. Yes, Thm 1 in the quoted reference is, if I get it right: if $T : \ell_p \to \ell_q$ is bounded, $1 < p, q < \infty$, $1/p + 1/q < 1$, then, writing $T$ as a matrix for the standard basis, the double series $\langle T x, y \rangle$ converges, and does so uniformly in $(x, y) \in \ell_p \times \ell_q$. – user66081 Jan 24 '14 at 08:42
  • A generalization is in "On quasi-complemented subspaces of Banach spaces, with an Appendix on compactness of operators from $L^p(\mu)$ to $L^r(\nu)$", J of Functional Analysis, Vol 4, Issue 2, October 1969. It is along the lines of t.b.'s answer here http://math.stackexchange.com/questions/97126/if-1-leq-p-infty-then-show-that-lp0-1-and-ell-p-are-not-topologic – user66081 Jan 24 '14 at 09:04