Riesz-Thorin theorem

In mathematics, the Riesz-Thorin theorem, often referred to as the ``Riesz-Thorin Interpolation Theorem" or the ``Riesz-Thorin Convexity Theorem" is a result about

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``interpolation of operators".

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This should not be confused with somewhat different mathematical procedure of interpolation

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of functions.

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This theorem deals with linear maps acting between

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Lp spaces. Its usefulness stems from the fact that some of these spaces have rather simpler structure than others. Usually that refers to L^2 which is a Hilbert space, or to L^1 and L∞ (see examples below). Therefore one may prove theorems about the more complicated cases by proving them in two simple cases and then using the Riesz-Thorin theorem to pass from the simple cases to the complicated cases. A related approach is to use the Marcinkiewicz theorem.

Related Topics:
''L''^p - Usefulness - Hilbert space - Marcinkiewicz theorem

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