EUDML

In this paper we prove that for each $1 < p, \tilde{p} < \infty$ , the Banach space $(l^{\tilde{p}}, {∥\cdot∥}_{\tilde{p}})$ can be equivalently renormed in such a way that the Banach space $(l^{\tilde{p}}, {∥\cdot∥}_{L, α, β, p, \tilde{p}})$ is LUR and has a diametrically complete set with empty interior. This result extends the Maluta theorem about existence of such a set in $l^{2}$ with the Day norm. We also show that the Banach space $(l^{\tilde{p}}, {∥\cdot∥}_{L, α, β, p, \tilde{p}})$ has the weak fixed point property for nonexpansive mappings.

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Local uniform linear convexity with respect to the Kobayashi distance.

Domains which are locally uniformly linearly convex in the Kobayashi distance.

Infinite products of holomorphic mappings.

Uniform asymptotic normal structure, the uniform semi-Opial property and fixed points of asymptotically regular uniformly Lipschitzian semigroups. I.

Uniform asymptotic normal structure, the uniform semi-opial property, and fixed points of asymptotically regular uniformly Lipschitzian semigroups. II.

The generalized Day norm. Part I. Properties

The generalized Day norm. Part II. Applications