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Interpolation of compact operators by the methods of Calderón and Gustavsson–Peetre

Published online by Cambridge University Press:  20 January 2009

M. Cwikel  and
N. J. Kalton
M. Cwikel
Affiliation:
Department of Mathematics, Technion, Israel Institute of Technology, Haifa 3200, Israel
N. J. Kalton
Affiliation:
Department of Mathematics, University of Missouri-Columbia, Columbia, Missouri 65211, USA
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Abstract

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Let X = (X0, X1) and Y = (Y0, Y1) be Banach couples and suppose T:X→Y is a linear operator such that T:X0→Y0 is compact. We consider the question whether the operator T:[X0, X1]θ→[Y0, Y1]θ is compact and show a positive answer under a variety of conditions. For example it suffices that X0 be a UMD-space or that X0 is reflexive and there is a Banach space so that X0 = [W, X1]α, for some 0<α<1.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 38 , Issue 2 , June 1995 , pp. 261 - 276
Copyright
Copyright © Edinburgh Mathematical Society 1995

References

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