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 $(K,d)$ the Banach space \Lip(K) consists of all scalar-valued bounded Lipschitz functions on $K$ with the norm $\|f\|_{L}=\max(\|f\|_{\infty},L(f))$, where $L(f)$ is the Lipschitz constant of $f$. The closed subspace \lip(K) of \Lip(K) contains all elements of \Lip(K) satisfying the \lip-condition $\lim_{0<d(x,y)\to 0}|f(x)-f(y)|/d(x,y)=0$. For $K=([0,1],| {\cdot} |^{\alpha})$, $0<\alpha<1$, we prove that \lip(K) is a proper $M$-ideal in a certain subspace of \Lip(K) containing a copy of $\ell^{\infty}$.Comment: Includes 4 figure

The Daugavet equation for operators not fixing a copy of C(S)C(S)

We prove the norm identity $\|Id+T\| = 1+\|T\|$, which is known as the Daugavet equation, for operators $T$ on $C(S)$ not fixing a copy of $C(S)$, where $S$ is a compact metric space without isolated points

Classical magnetic Lifshits tails in three space dimensions: impurity potentials with slow anisotropic decay

We determine the leading low-energy fall-off of the integrated density of states of a magnetic Schroedinger operator with repulsive Poissonian random potential in case its single impurity potential has a slow anisotropic decay at infinity. This so-called magnetic Lifshits tail is shown to coincide with the one of the corresponding classical integrated density of states