On the fixed point property in direct sums of Banach spaces with strictly monotone norms

Stanisław Prus, and Andrzej Wiśnicki. "On the fixed point property in direct sums of Banach spaces with strictly monotone norms." Studia Mathematica 186.1 (2008): 87-99. <http://eudml.org/doc/284741>.

@article{StanisławPrus2008,
abstract = {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 WCS(Y) > 1), then X ⊕ 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.},
author = {Stanisław Prus, Andrzej Wiśnicki},
journal = {Studia Mathematica},
keywords = {fixed point property; nonexpansive mapping; direct sum; asymptotic (P); Banach-Saks property; unconditional basis},
language = {eng},
number = {1},
pages = {87-99},
title = {On the fixed point property in direct sums of Banach spaces with strictly monotone norms},
url = {http://eudml.org/doc/284741},
volume = {186},
year = {2008},
}

TY - JOUR
AU - Stanisław Prus
AU - Andrzej Wiśnicki
TI - On the fixed point property in direct sums of Banach spaces with strictly monotone norms
JO - Studia Mathematica
PY - 2008
VL - 186
IS - 1
SP - 87
EP - 99
AB - 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 WCS(Y) > 1), then X ⊕ 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.
LA - eng
KW - fixed point property; nonexpansive mapping; direct sum; asymptotic (P); Banach-Saks property; unconditional basis
UR - http://eudml.org/doc/284741
ER -