Skip to main content
×
Home
    • Aa
    • Aa

TENSOR EXTENSION PROPERTIES OF C(K)-REPRESENTATIONS AND APPLICATIONS TO UNCONDITIONALITY

  • CHRISTOPH KRIEGLER (a1) (a2) and CHRISTIAN LE MERDY (a3)
Abstract
Abstract

Let K be any compact set. The C*-algebra C(K) is nuclear and any bounded homomorphism from C(K) into B(H), the algebra of all bounded operators on some Hilbert space H, is automatically completely bounded. We prove extensions of these results to the Banach space setting, using the key concept ofR-boundedness. Then we apply these results to operators with a uniformly bounded H-calculus, as well as to unconditionality on Lp. We show that any unconditional basis on Lp ‘is’ an unconditional basis on L2 after an appropriate change of density.

  • View HTML
    • 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.

      TENSOR EXTENSION PROPERTIES OF C(K)-REPRESENTATIONS AND APPLICATIONS TO UNCONDITIONALITY
      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.

      TENSOR EXTENSION PROPERTIES OF C(K)-REPRESENTATIONS AND APPLICATIONS TO UNCONDITIONALITY
      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.

      TENSOR EXTENSION PROPERTIES OF C(K)-REPRESENTATIONS AND APPLICATIONS TO UNCONDITIONALITY
      Available formats
      ×
Copyright
Corresponding author
For correspondence; e-mail: christoph.kriegler@univ-fcomte.fr
Footnotes
Hide All

The first author is supported by the Karlsruhe House of Young Scientists and the Franco-German University DFH-UFA, the second author is supported by the research program ANR-06-BLAN-0015.

Footnotes
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1] W. Arendt and S. Bu , ‘The operator-valued Marcinkiewicz multiplier theorem and maximal regularity’, Math. Z. 240 (2002), 311343.

[3] J. W. Bunce , ‘Representations of strongly amenable C*-algebras’, Proc. Amer. Math. Soc. 32 (1972), 241246.

[8] B. de Pagter and W. J. Ricker , ‘C(K)-representations and R-boundedness’, J. London Math. Soc. 76 (2007), 498512.

[10] J. Diestel and J. J. Uhl , Vector Measures, Mathematical Surveys and Monographs, 15 (American Mathematical Society, Providence, RI, 1977).

[11] I. Doust and R. deLaubenfels , ‘Functional calculus, integral representations, and Banach space geometry’, Quaestiones Math. 17 (1994), 161171.

[14] E. Effros and Z.-J. Ruan , ‘On matricially normed spaces’, Pacific J. Math. 132 (1988), 243264.

[17] M. Hoffmann , N. J. Kalton and T. Kucherenko , ‘R-bounded approximating sequences and applications to semigroups’, J. Math. Anal. Appl. 294 (2004), 373386.

[18] W. B. Johnson and L. Jones , ‘Every Lp operator is an L2 operator’, Proc. Amer. Math. Soc. 72 (1978), 309312.

[20] N. J. Kalton and G. Lancien , ‘A solution to the problem of Lp-maximal regularity’, Math. Z. 235 (2000), 559568.

[21] N. J. Kalton and L. Weis , ‘The H-calculus and sums of closed operators’, Math. Ann. 321 (2001), 319345.

[23] P. C. Kunstmann and L. Weis , ‘Maximal Lp-regularity for parabolic equations, Fourier multiplier theorems and H-functional calculus’, in: Functional Analytic Methods for Evolution Equations, Lecture Notes in Mathematics, 1855 (Springer, New York, 2004), pp. 65311.

[25] C. Le Merdy , ‘A strong similarity property of nuclear C*-algebras’, Rocky Mountain J. Math. 30 (2000), 279292.

[26] C. Le Merdy and A. Simard , ‘A factorization property of R-bounded sets of operators on Lp-spaces’, Math. Nachr. 243 (2002), 146155.

[27] J. Lindenstrauss and L. Tzafriri , Classical Banach Spaces I (Springer, Berlin, 1977).

[30] G. Pisier , Similarity Problems and Completely Bounded Maps (Second, expanded version), Lecture Notes in Mathematics, 1618 (Springer, New York, 2001).

[31] W. J. Ricker , Operator Algebras Generated by Commuting Projections: A Vector Measure Approach, Lecture Notes in Mathematics, 1711 (Springer, New York, 1999).

Recommend this journal

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

Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords:

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 19 *
Loading metrics...

Abstract views

Total abstract views: 57 *
Loading metrics...

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