Jean-Matthieu Aug'e

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math.FA2012

Perturbation of farthest points in weakly compact sets

Jean-Matthieu Augé

If $f$ is a real valued weakly lower semi-continous function on a Banach space $X$ and $C$ a weakly compact subset of $X$ , we show that the set of $x \in X$ such that $z \mapsto \|…

math.FA2012

Orbits of linear operators and Banach space geometry

Jean-Matthieu Augé

Let $T$ be a bounded linear operator on a (real or complex) Banach space $X$ . If $(a_{n})$ is a sequence of non-negative numbers tending to 0. Then, the set of $x \in X$ such that $\…

math.FA2012

Linear operators with wild dynamics

Jean-Matthieu Augé

If $X$ is a separable infinite dimensional Banach space, we construct a bounded and linear operator $R$ on $X$ such that $A_{R} = {x \in X, ∥ R^{t} x ∥ \to \infty}$ is not d…