Kadec Norms on Spaces of Continuous Functions

Burke, Maxim R., Wiesaw, Kubis, and Stevo, Todorcevic. "Kadec Norms on Spaces of Continuous Functions." Serdica Mathematical Journal 32.2-3 (2006): 227-258. <http://eudml.org/doc/281530>.

@article{Burke2006,
abstract = {2000 Mathematics Subject Classification: Primary: 46B03, 46B26. Secondary: 46E15, 54C35.We study the existence of pointwise Kadec renormings for Banach spaces of the form C(K). We show in particular that such a renorming exists when K is any product of compact linearly ordered spaces, extending the result for a single factor due to Haydon, Jayne, Namioka and Rogers. We show that if C(K1) has a pointwise Kadec renorming and K2 belongs to the class of spaces obtained by closing the class of compact metrizable spaces under inverse limits of transfinite continuous sequences of retractions, then C(K1×K2) has a pointwise Kadec renorming. We also prove a version of the three-space property for such renormings.},
author = {Burke, Maxim R., Wiesaw, Kubis, Stevo, Todorcevic},
journal = {Serdica Mathematical Journal},
keywords = {tp-Kadec Norm; Banach Space of Continuous Functions; Compact Space; Banach space of continuous functions; compact space},
language = {eng},
number = {2-3},
pages = {227-258},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Kadec Norms on Spaces of Continuous Functions},
url = {http://eudml.org/doc/281530},
volume = {32},
year = {2006},
}

TY - JOUR
AU - Burke, Maxim R.
AU - Wiesaw, Kubis
AU - Stevo, Todorcevic
TI - Kadec Norms on Spaces of Continuous Functions
JO - Serdica Mathematical Journal
PY - 2006
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 32
IS - 2-3
SP - 227
EP - 258
AB - 2000 Mathematics Subject Classification: Primary: 46B03, 46B26. Secondary: 46E15, 54C35.We study the existence of pointwise Kadec renormings for Banach spaces of the form C(K). We show in particular that such a renorming exists when K is any product of compact linearly ordered spaces, extending the result for a single factor due to Haydon, Jayne, Namioka and Rogers. We show that if C(K1) has a pointwise Kadec renorming and K2 belongs to the class of spaces obtained by closing the class of compact metrizable spaces under inverse limits of transfinite continuous sequences of retractions, then C(K1×K2) has a pointwise Kadec renorming. We also prove a version of the three-space property for such renormings.
LA - eng
KW - tp-Kadec Norm; Banach Space of Continuous Functions; Compact Space; Banach space of continuous functions; compact space
UR - http://eudml.org/doc/281530
ER -