# Kadec Norms on Spaces of Continuous Functions

Burke, Maxim R.; Wiesaw, Kubis; Stevo, Todorcevic

Serdica Mathematical Journal (2006)

- Volume: 32, Issue: 2-3, page 227-258
- ISSN: 1310-6600

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topBurke, 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 -

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