Complex interpolation and convexity

Vignati, Marco

doi:10.1090/S0002-9939-1987-0877044-2

Complex interpolation and convexity
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by Marco Vignati

Proc. Amer. Math. Soc. 99 (1987), 705-711

DOI: https://doi.org/10.1090/S0002-9939-1987-0877044-2

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Abstract:

The relations between the complex theory of interpolation for families of Banach spaces and the notion of uniform convexity are studied. It is proven that the moduli of uniform convexity vary smoothly with the interpolation spaces. A new notion of "distance" between Banach spaces is introduced.

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