Skip to main content Accessibility help
×
Home

Isometric Stability Property of Certain Banach Spaces

  • Alexander Koldobsky (a1)

Abstract

Let E be one of the spaces C(K) and L 1, F be an arbitrary Banach space, p > 1, and (X, σ) be a space with a finite measure. We prove that E is isometric to a subspace of the Lebesgue-Bochner space LP(X; F) only if E is isometric to a subspace of F. Moreover, every isometry T from E into Lp(X; F) has the form Te(x) = h(x)U(x)e, eE, where h: X —> R is a measurable function and, for every x ∊ X, U(x) is an isometry from E to F

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Isometric Stability Property of Certain Banach Spaces
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Isometric Stability Property of Certain Banach Spaces
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Isometric Stability Property of Certain Banach Spaces
      Available formats
      ×

Copyright

References

Hide All
1. Bourgain, J., An averaging result for c0-sequences, Bull. Soc. Math. Belg. Sér. B 30(1978), 8387.
2. Dowling, P. N., A stability property of a class of Banach spaces not containing c$, Canad. Math. Bull. 35(1992), 5660.
3. Emmanuele, G., Copies of l in Köthe spaces of vector valued functions, Illinois J. Math. 36(1992), 293 296.
4. Koldobsky, A., Isometries of Lp(X;Lq) and equimeasurability', Indiana Univ. Math. J. 40(1991), 677705.
5. Koldobsky, A., Measures on spaces of operators and isometries, J. Soviet Math. 42(1988), 16281636.
6. Kwapien, S., On Banach spaces containing CQ, Studia Math. 52(1974), 187188.
7. Mendoza, J., Copies of l in Lp(μ;X), Proc. Amer. Math. Soc. 109(1990), 125127.
8. Pisier, G., Une propriété de stabilité de la classe des espaces ne contenant pas l1 , Acad, C. R.. Sci. Paris Sér. A 86(1978), 747749.
9. Raynaud, Y., Sous espaces lr et géométrie des espaces LP(Lq) et Lϕ , Acad, C. R.. Sci. Paris Sér. I Math. 301(1985), 299302.
10. Saab, E. and Saab, P., On stability problems of some properties in Banach spaces, Function spaces (ed. Jarosz, K.), Lecture Notes in Pure and Appl. Math. 136(1992), 367394.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Keywords

Isometric Stability Property of Certain Banach Spaces

  • Alexander Koldobsky (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed