Skip to main content Accessibility help
×
Home

ON A FUNCTION MODULE WITH APPROXIMATE HYPERPLANE SERIES PROPERTY

  • T. GRANDO (a1) and M. L. LOURENÇO (a2)

Abstract

We present a sufficient and necessary condition for a function module space $X$ to have the approximate hyperplane series property (AHSP). As a consequence, we have that the space ${\mathcal{C}}_{0}(L,E)$ of bounded and continuous $E$ -valued mappings defined on the locally compact Hausdorff space $L$ has AHSP if and only if $E$ has AHSP.

    • 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.

      ON A FUNCTION MODULE WITH APPROXIMATE HYPERPLANE SERIES PROPERTY
      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.

      ON A FUNCTION MODULE WITH APPROXIMATE HYPERPLANE SERIES PROPERTY
      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.

      ON A FUNCTION MODULE WITH APPROXIMATE HYPERPLANE SERIES PROPERTY
      Available formats
      ×

Copyright

Corresponding author

References

Hide All
[1]Acosta, M. D., Aron, R. M., García, D. and Maestre, M., ‘The Bishop–Phelps–Bollobás theorem for operators’, J. Funct. Anal. 254 (2008), 27802799.
[2]Acosta, M. D., Becerra-Guerrero, J., Choi, Y. S., Ciesielski, M., Kim, S. K., Lee, H. J., Lourenço, M. L. and Martín, M., ‘The Bishop–Phelps–Bollobás property for operators between spaces of continuous functions’, Nonlinear Anal. 95 (2014), 323332.
[3]Acosta, M. D., Becerra-Guerrero, J., García, D., Kim, S. K. and Maestre, M., ‘Bishop–Phelps–Bollobás property for certain spaces of operators’, J. Math. Anal. Appl. 414 (2014), 532545.
[4]Aron, R. M., Cascales, B. and Kozhushkina, O., ‘The Bishop–Phelps–Bollobás theorem and Asplund operators’, Proc. Amer. Math. Soc. 139(10) (2011), 35533560.
[5]Aron, R. M., Choi, Y. S., García, D. and Maestre, M., ‘The Bishop–Phelps–Bollobás theorem for 𝓛(L 1(𝜇), L [0, 1])’, Adv. Math. 228(1) (2011), 617628.
[6]Aron, R. M., Choi, Y. S., Kim, S. K., Lee, H. J. and Martín, M., ‘The Bishop–Phelps–Bollobás version of Lindenstrauss properties A and B’, Trans. Amer. Math. Soc. 367 (2015), 60856101.
[7]Behrends, E., M-Structure and the Banach–Stone Theorem (Springer, Berlin, 1979).
[8]Bishop, E. and Phelps, R. R., ‘A proof that every Banach space is subreflexive’, Bull. Amer. Math. Soc. (N.S.) 67 (1961), 9798.
[9]Bollobás, B., ‘An extension to the theorem of Bishop and Phelps’, Bull. Lond. Math. Soc. 2 (1970), 181182.
[10]Cascales, B., Guirao, A. J. and Kadets, V., ‘A Bishop–Phelps–Bollobás type theorem for uniform algebras’, Adv. Math. 240 (2013), 370382.
[11]Chica, M., Kadets, V., Martín, M., Moreno-Pulido, S. and Rambla-Barreno, F., ‘Bishop–Phelps–Bollobás moduli of a Banach space’, J. Math. Anal. Appl. 412(2) (2014), 697719.
[12]Choi, Y. S. and Kim, S. K., ‘The Bishop–Phelps–Bollobás theorem for operators from L 1(𝜇) to Banach spaces with the Radon–Nikodým property’, J. Funct. Anal. 261(6) (2011), 14461456.
[13]Choi, Y. S. and Kim, S. K., ‘The Bishop–Phelps–Bollobás property and lush spaces’, J. Math. Anal. Appl. 390 (2012), 549555.
[14]Choi, Y. S., Kim, S. K., Lee, H. J. and Martín, M., ‘The Bishop–Phelps–Bollobás theorem for operators on L 1(𝜇)’, J. Funct. Anal. 267(91) (2014), 214242.
[15]Choi, Y. S., Kim, S. K., Lee, H. J. and Martín, M., ‘On Banach spaces with the approximate hyperplane series property’, Banach J. Math. Anal. 9(4) (2015), 243258.
[16]Kim, S. K., ‘The Bishop–Phelps–Bollobás theorem for operators from c 0 to uniformly convex spaces’, Israel J. Math. 197(1) (2013), 425435.
[17]Kim, S. K. and Lee, H. J., ‘Uniform convexity and Bishop–Phelps–Bollobás property’, Canad. J. Math. 66(2) (2014), 372386.
[18]Lindenstrauss, J., ‘On operators which attain their norm’, Israel J. Math. 1 (1963), 139148.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Keywords

MSC classification

ON A FUNCTION MODULE WITH APPROXIMATE HYPERPLANE SERIES PROPERTY

  • T. GRANDO (a1) and M. L. LOURENÇO (a2)

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.