Skip to main content
×
Home
    • Aa
    • Aa

A counterexample using 4-linear forms

  • David Pérez-García (a1)
Abstract

We prove that, for n ≥ 4 and arbitrary infinite dimensional Banach spaces X1,…Xn, there exists an extendible n-linear form T: X1 x…x Xn →  that is not integral.

    • 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.

      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.

      A counterexample using 4-linear forms
      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 Dropbox account. Find out more about sending content to Dropbox.

      A counterexample using 4-linear forms
      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 Google Drive account. Find out more about sending content to Google Drive.

      A counterexample using 4-linear forms
      Available formats
      ×
Copyright
References
Hide All
[1]Arens R., ‘The adjoint of a bilinear operator’, Proc. Amer. Math. Soc. 2 (1951), 839848.
[2]Arens R., ‘Operations induced in function classes’, Monatsh. Math. 55 (1951), 119.
[3]Aron R. and Berner P.D., ‘A Hahn-Banach extension theorem for analytic mappings’, Bull. Soc. Math. France 106 (1978), 324.
[4]Cabello F., García R. and Villanueva I., ‘Extension of multilinear operators on Banach spaces’, Extracta Math. 15 (2000), 291334.
[5]Carando D., ‘Extendibility of polynomials and analytic functions on ℓp’, Studia Math. 145 (2001), 6373.
[6]Carando D. and Zalduendo I., ‘A Hahn-Banach theorem for integral polynomials’, Proc. Amer. Math. Soc. 127 (1999), 241250.
[7]Castillo J.M.F., García R., and Jaramillo J.A., ‘Extensions of bilinear forms on Banach spaces’, Proc. Amer. Math. Soc. 129 (2001), 36473656.
[8]Defant A. and Floret K., Tensor norms and operator ideals, North Holland Math. Studies 176 (North-Holland Publishing Co., Amsterdam, 1993).
[9]Diestel J., Jarchow H., and Tonge A., Absolutely summing operators (Cambridge Univ. Press, Cambridge, 1995).
[10]Kalton N., ‘Locally complemented subspaces and ℒp-spaces for 0 < p < 1’, Math. Nachr. 115 (7197).
[11]Kirwan P. and Ryan R., ‘Extendibility of homogeneous polynomials on Banach spaces’, Proc. Amer. Math. Soc. 124 (1998), 10231029.
[12]Lindström M. and Ryan R., ‘Applications of ultraproducts to infinite dimensional holomorphy’, Math. Scand. 71 (1992), 229242.
[13]Ryan R. A., ‘Dunford-Pettis properties’, Bull. Acad. Polon. Sci. Ser. Sci. Math. 27 (1979), 373379.
[14]Schütt C., ‘Unconditionality in tensor products’, Israel J. Math. 31 (1978), 209216.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 11 *
Loading metrics...

Abstract views

Total abstract views: 14 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 19th October 2017. This data will be updated every 24 hours.