Nigel John Kalton's Books

In the manner described in the introduction we show the existence of value for all two person, zero-sum differential games of prescribed duration. Using the concept of relaxed controls from control theory we relate the approaches to differential games of A. Friedman and W. Fleming. We show that if the 'Isaacs' condition' is satisfied then the game has a value in the sense of Friedman. Over the relaxed controls Isaacs' condition is always satisfied and so the game always has a value in this setting. We do not need Friedman's hypothesis that the two sets of control variables appear separated in the dynamical equations and payoff. The introduction of probabilistic ideas into differential games by relaxed controls thus gives a value, as the introduction of mixed strategies by von Neumann does for two person zero-sum matrix games.

The general problem addressed in this work is to characterize the possible Banach lattice structures that a separable Banach space may have. The basic questions of uniqueness of lattice structure for function spaces have been studied before, but here the approach uses random measure representations for operators in a new way to obtain more powerful conclusions.

Recently, Jawerth, Rochberg and Weiss have studied nonlinear maps arising from interpolation theory which satisfy commutator relationships with interpolated linear operators. Here we present a very general result of this type for rearrangement-invariant Banach function spaces.

Book's by Nigel John Kalton

The Existence of Value in Differential Games

The Existence of Value in Differential Games

Lattice Structures on Banach Spaces

Lattice Structures on Banach Spaces

Nonlinear Commutators in Interpolation Theory

Nonlinear Commutators in Interpolation Theory

Nonlinear Commutators in Interpolation Theory

Nonlinear Commutators in Interpolation Theory

Nonlinear Commutators in Interpolation Theory

Nonlinear Commutators in Interpolation Theory

Lattice Structures on Banach Spaces

Lattice Structures on Banach Spaces

Lattice Structures on Banach Spaces

Lattice Structures on Banach Spaces

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