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Nigel Kalton's work in isometrical Banach space theory
This paper surveys some of the late Nigel Kalton's contributions to Banach
space theory. The paper is written for the Nigel Kalton Memorial Website
http://mathematics.missouri.edu/kalton/, which is scheduled to go online in
summer 2011
Lipschitz spaces and M-ideals
For a metric space the Banach space \Lip(K) consists of all
scalar-valued bounded Lipschitz functions on with the norm
, where is the Lipschitz constant
of . The closed subspace \lip(K) of \Lip(K) contains all elements of
\Lip(K) satisfying the \lip-condition . For , , we
prove that \lip(K) is a proper -ideal in a certain subspace of \Lip(K)
containing a copy of .Comment: Includes 4 figure
The Daugavet equation for operators not fixing a copy of
We prove the norm identity , which is known as the
Daugavet equation, for operators on not fixing a copy of ,
where is a compact metric space without isolated points
Remarks on rich subspaces of Banach spaces
We investigate rich subspaces of and deduce an interpolation property
of Sidon sets.
We also present examples of rich separable subspaces of nonseparable Banach
spaces and we study the Daugavet property of tensor products.Comment: 12 page
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