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Type and Cotype of Normed Spaces, and Some Simple Relations with Geometrical Properties

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Part of the Lecture Notes in Mathematics book series (LNM, volume 1200)

Abstract

Let X be a normed space, x i X, i = 1,2,... . In this section we will study the averages \( \left( {\mathop {Ave}\limits_{\varepsilon _i = \pm 1} \left\| {\sum\nolimits_{i = 1}^n {\varepsilon _i x_i } } \right\|^2 } \right)^{1/2} \) and see that the order of magnitude of these averages gives a lot of information about some geometrical properties of X.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

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