Extreme non-Arens regularity of quotients of the Fourier algebra A(G)

Zhiguo Hu

Colloquium Mathematicae (1997)

  • Volume: 72, Issue: 2, page 237-249
  • ISSN: 0010-1354

How to cite

top

Hu, Zhiguo. "Extreme non-Arens regularity of quotients of the Fourier algebra A(G)." Colloquium Mathematicae 72.2 (1997): 237-249. <http://eudml.org/doc/210462>.

@article{Hu1997,
author = {Hu, Zhiguo},
journal = {Colloquium Mathematicae},
keywords = {Arens regularity; Banach algebra; almost periodic functionals; Fourier algebra; locally compact group; von Neumann algebra; extreme non-ergodicity},
language = {eng},
number = {2},
pages = {237-249},
title = {Extreme non-Arens regularity of quotients of the Fourier algebra A(G)},
url = {http://eudml.org/doc/210462},
volume = {72},
year = {1997},
}

TY - JOUR
AU - Hu, Zhiguo
TI - Extreme non-Arens regularity of quotients of the Fourier algebra A(G)
JO - Colloquium Mathematicae
PY - 1997
VL - 72
IS - 2
SP - 237
EP - 249
LA - eng
KW - Arens regularity; Banach algebra; almost periodic functionals; Fourier algebra; locally compact group; von Neumann algebra; extreme non-ergodicity
UR - http://eudml.org/doc/210462
ER -

References

top
  1. [1] R. Arens, The adjoint of a bilinear operation, Proc. Amer. Math. Soc. 2 (1951), 839-848. Zbl0044.32601
  2. [2] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, New York, 1973. Zbl0271.46039
  3. [3] C. Chou, Topological invariant means on the von Neumann algebra VN(G), Trans. Amer. Math. Soc. 273 (1982), 207-229. Zbl0507.22007
  4. [4] J. Duncan and S. A. R. Hosseinium, The second dual of a Banach algebra, Proc. Roy. Soc. Edinburgh 84A (1979), 309-325. Zbl0427.46028
  5. [5] C. Dunkl and D. Ramirez, Weakly almost periodic functionals on the Fourier algebra, Trans. Amer. Math. Soc. 185 (1973), 501-514. 
  6. [6] P. Eymard, L'algèbre de Fourier d'un groupe localement compact, Bull. Soc. Math. France 92 (1964), 181-236. Zbl0169.46403
  7. [7] B. Forrest, Amenability and bounded approximate identities in ideals of A(G), Illinois J. Math. 34 (1990), 1-25. Zbl0712.43002
  8. [8] B. Forrest, Arens regularity and discrete groups, Pacific J. Math. 151 (1991), 217-227. Zbl0746.43002
  9. [9] B. Forrest, Arens regularity and the A p ( G ) algebras, Proc. Amer. Math. Soc. 119 (1993), 595-598. 
  10. [10] E. E. Granirer, Weakly almost periodic and uniformly continuous functionals on the Fourier algebra of any locally compact group, Trans. Amer. Math. Soc. 189 (1974), 371-382. Zbl0292.43015
  11. [11] E. E. Granirer, On some properties of the Banach algebras A p ( G ) for locally compact groups, Proc. Amer. Math. Soc. 95 (1985), 375-381. Zbl0599.43005
  12. [12] E. E. Granirer, On convolution operators with small support which are far from being convolution by a bounded measure, Colloq. Math. 67 (1994), 33-60; Erratum, 69 (1995), 155. Zbl0841.43008
  13. [13] E. E. Granirer, Day points for quotients of the Fourier algebra A(G), extreme nonergodicity of their duals and extreme non-Arens regularity, Illinois J. Math., to appear. Zbl0855.43004
  14. [14] E. E. Granirer, On the set of topologically invariant means on an algebra of convolution operators on L p ( G ) , Proc. Amer. Math. Soc., to appear. Zbl0853.43007
  15. [15] E. Hewitt and K. A. Ross, Abstract Harmonic Analysis I, Springer, New York, 1979. Zbl0416.43001
  16. [16] Z. Hu, On the set of topologically invariant means on the von Neumann algebra VN(G), Illinois J. Math. 39 (1995), 463-490. Zbl0840.22012
  17. [17] Z. Hu, The von Neumann algebra VN(G) of a locally compact group and quotients of its subspaces, preprint. Zbl0905.22006
  18. [18] A. T. Lau, The second conjugate of the Fourier algebra of a locally compact group, Trans. Amer. Math. Soc. 267 (1981), 53-63. Zbl0489.43006
  19. [19] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces, Vol. I, Springer, 1977. Zbl0362.46013
  20. [20] K. Musiał, The weak Radon-Nikodym property in Banach spaces, Studia Math. 54 (1979), 151-173. Zbl0405.46015
  21. [21] J. S. Pym, The convolution of functionals on spaces of bounded functions, Proc. London Math. Soc. 15 (1965), 84-104. Zbl0135.35503
  22. [22] A. Ülger, Arens regularity sometimes implies the RNP, Pacific J. Math. 143 (1990), 377-399. Zbl0734.46032

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.