Perturbations of isometries between C(K)-spaces

• Autorzy: Yves Dutrieux , Nigel J. Kalton
• Języki publikacji: EN

Abstrakty

EN

We study the Gromov-Hausdorff and Kadets distances between C(K)-spaces and their quotients. We prove that if the Gromov-Hausdorff distance between C(K) and C(L) is less than 1/16 then K and L are homeomorphic. If the Kadets distance is less than one, and K and L are metrizable, then C(K) and C(L) are linearly isomorphic. For K and L countable, if C(L) has a subquotient which is close enough to C(K) in the Gromov-Hausdorff sense then K is homeomorphic to a clopen subset of L.

Kategorie tematyczne

• 46E15: Banach spaces of continuous, differentiable or analytic functions
• 46T99: None of the above, but in this section
• 46B26: Nonseparable Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2005
• Tom: 166
• Numer: 2
• Strony: 181-197

Daty

wydano

2005

Twórcy

autor

Yves Dutrieux

• Laboratoire de Mathématiques, UMR 6623, Université de Franche-Comté, 25030 Besançon Cedex, France

autor

Nigel J. Kalton

• Department of Mathematics, University of Missouri-Columbia, Columbia, MO 65211, U.S.A.

Identyfikatory

DOI

10.4064/sm166-2-4