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Journal of the London Mathematical Society 2001 63(2):453-468; doi:10.1017/S0024610700001861
© 2001 by London Mathematical Society
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© The London Mathematical Society

Operators of Rademacher and Gaussian Subcotype

Aicke Hinrichs

Mathematisches Institut, Friedrich-Schiller-Universität Jena D-07743 Jena, Germany, nah{at}rz.uni-jena.de

Received 4 June 1998.

For a linear and bounded operator T from a Banach space X into a Banach space Y, let {varrho}(T|In, Rn) and {varrho}(T|In, Gn) denote the Rademacher and Gaussian cotype 2 norm of T computed with n vectors, respectively. It is shown that the sequence {varrho}(T|In, Rn) has submaximal behaviour if and only if {varrho}(T|In, Gn) has. This means that


Formula

Moreover, the class of these operators coincides with the class of operators preserving copies of Formula uniformly. The tool connecting these concepts is the equal norm Rademacher cotype of operators.


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