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On sequences not enjoying Schur’s property

100%

Jiménez-Rodríguez P.

Open Mathematics

2017

tom 15

nr 1

233-237

Here we proved the existence of a closed vector space of sequences - any nonzero element of which does not comply with Schur’s property, that is, it is weakly convergent but not norm convergent. This allows us to find similar algebraic structures in some subsets of functions.

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Weak nearly uniform smoothness of the \(\psi\)-direct sums \((X_1 \oplus \dots\oplus X_N)_\psi\)

75%

Kato M., Tamura T.

Commentationes Mathematicae

2012

tom 52

nr 2

We shall characterize the weak nearly uniform smoothness of the \(\psi\)-direct sum \((X_1\oplus \dots\oplus X_N)_\psi\) of \(N\) Banach spaces \(X_1,\dots,X_N\), where \(\psi\) is a convex function satisfying certain conditions on the convex set \(\Delta_N = \{(s_1 ,\dots , s_{N-1})\in \mathbb{R}_+^{N-1} : \sum_{i=1}^{N-1} s_i \leq 1\). To do this a class of convex functions which yield \(\ell_1\)-like norms will be introduced. We shall apply our result to the fixed point property for nonexpansive mappings (FPP). In particular an example will be presented which indicates that there are plenty of Banach spaces with FPP failing to be uniformly non-square.

Weak nearly uniform soothness and worth property of \(\psi\)-direct sums of Banach spaces

63%

Kato M., Tamura T.

Commentationes Mathematicae

2006

tom 46

nr 1

We shall characterize the weak nearly uniform smoothness of the \(\psi\)-direct sum \(X \oplus_\psi Y\) of Banach spaces \(X\) and \(Y\). The Schur and WORTH properties will be also characterized. As a consequence we shall see in the \(\ell_\infty\)-sums of Banach spaces there are many examples of Banach spaces with the fixed point property which are not uniformly non-square.

Ograniczanie wyników

2 Commentationes Mathematicae

1 Open Mathematics

2 Kato M.

2 Tamura T.

1 Jiménez-Rodríguez P.

1 2017

1 2012

1 2006

Wyniki wyszukiwania

On sequences not enjoying Schur’s property

Weak nearly uniform smoothness of the \(\psi\)-direct sums \((X_1 \oplus \dots\oplus X_N)_\psi\)

Weak nearly uniform soothness and worth property of \(\psi\)-direct sums of Banach spaces