Geodesic
On the fixed point property in direct sums of Banach spaces with strictly monotone norms
Stanis/law Prus1 ; Andrzej Wi/snicki1
1 Institute of Mathematics Maria Curie-Sk/lodowska University 20-031 Lublin, Poland
Studia Mathematica, Tome 186 (2008) no. 1, pp. 87-99

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

It is shown that if a Banach space $X$ has the weak Banach–Saks property and the weak fixed point property for nonexpansive mappings and $Y$ has the asymptotic (P) property (which is weaker than the condition ${\rm WCS}( Y) >1$), then $X\oplus Y$ endowed with a strictly monotone norm enjoys the weak fixed point property. The same conclusion is valid if $X$ admits a $1$-unconditional basis.
DOI : 10.4064/sm186-1-8
Keywords: shown banach space has weak banach saks property weak fixed point property nonexpansive mappings has asymptotic property which weaker condition wcs oplus endowed strictly monotone norm enjoys weak fixed point property conclusion valid admits unconditional basis

Stanis/law Prus 1 ; Andrzej Wi/snicki 1

1 Institute of Mathematics Maria Curie-Sk/lodowska University 20-031 Lublin, Poland 
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Stanis/law Prus; Andrzej Wi/snicki. On the fixed point property in direct sums of Banach spaces
 with strictly monotone norms. Studia Mathematica, Tome 186 (2008) no. 1, pp. 87-99. doi: 10.4064/sm186-1-8

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