Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: uniform Kadec-Klee property

Sortuj według:

Ogranicz wyniki do:

Banach-Saks property in some Banach sequence spaces

100%

Cui Y., Hudzik H., Płuciennik R.

Annales Polonici Mathematici

1996-1997

tom 65

nr 2

193-202

It is proved that for any Banach space X property (β) defined by Rolewicz in [22] implies that both X and X* have the Banach-Saks property. Moreover, in Musielak-Orlicz sequence spaces, criteria for the Banach-Saks property, the near uniform convexity, the uniform Kadec-Klee property and property (H) are given.

A new convexity property that implies a fixed point property for $L_{1}$

84%

Lennard C.

Studia Mathematica

1991

tom 100

nr 2

95-108

In this paper we prove a new convexity property for L₁ that resembles uniform convexity. We then develop a general theory that leads from the convexity property through normal structure to a fixed point property, via a theorem of Kirk. Applying this theory to L₁, we get the following type of normal structure: any convex subset of L₁ of positive diameter that is compact for the topology of convergence locally in measure, must have a radius that is smaller than its diameter. Indeed, a stronger result holds. The Chebyshev centre of any norm bounded, convergence locally in measure compact subset of L₁ must be norm compact. Immediately from normal structure, we get a new proof of a fixed point theorem for L₁ due to Lami Dozo and Turpin.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Studia Mathematica

1 Cui Y.

1 Hudzik H.

1 Lennard C.

1 Płuciennik R.

1 1997

1 1991

Wyniki wyszukiwania

Banach-Saks property in some Banach sequence spaces

A new convexity property that implies a fixed point property for $L_{1}$