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Some remarks on generalised lush spaces

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Hardtke J.-D.

Studia Mathematica

2015

tom 231

nr 1

29-44

D. Tan, X. Huang and R. Liu [Studia Math. 219 (2013)] recently introduced the notion of generalised lush (GL) spaces, which, at least for separable spaces, is a generalisation of the concept of lushness introduced by Boyko et al. [Math. Proc. Cambridge Philos. Soc. 142 (2007)]. The main result of D. Tan et al. is that every GL-space has the so called Mazur-Ulam property (MUP). In this note, we prove some further properties of GL-spaces, for example, every M-ideal in a GL-space is again a GL-space, ultraproducts of GL-spaces are again GL-spaces, and if the bidual X** of a Banach space X is GL, then X itself has the MUP.

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WORTH property, García-Falset coefficient and Opial property of infinite sums

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Hardtke J.-D.

Commentationes Mathematicae

2015

tom 55

nr 1

We prove some results concerning the WORTH pro\-perty and the Garc\'{i}a-Falset coefficient of absolute sums of infinitely many Banach spaces. Also, the Opial property/uniform Opial property of infinite \(\ell^p\)-sums is studied, and some properties analogous to the Opial property/uniform Opial property are discussed for Lebesgue\polishendash Bochner spaces \(L^p(\mu,X)\).

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1 Commentationes Mathematicae

1 Studia Mathematica

2 Hardtke J.-D.

2 2015

Wyniki wyszukiwania

Some remarks on generalised lush spaces

WORTH property, García-Falset coefficient and Opial property of infinite sums