Surveys in Mathematics and its Applications

ISSN 1842-6298
 Volume 1 (2006), 51 - 60

SOME ABSOLUTELY CONTINUOUS REPRESENTATIONS OF FUNCTION ALGEBRAS

Adina Juratoni

Abstract. In this paper we study some absolutely continuous representations of function algebras, which are weak ρ-spectral in the sense of [5] and [6], for a scalar ρ > 0. Precisely we investigate certain conditions for the existence of a spectral ρ-dilation of such representation. Among others we obtain different results which generalize the corresponding theorems of D. Gaşpar [3].

2000 Mathematics Subject Classification: 46J25, 47A20, 46J10.
Keywords: Uniform algebra, representation, spectral dilation.

Full text

References

  1. T. Gamelin, Uniform Algebras, Pretince-Hall, Englewood Cliffs, New Jersy,1969. MR0410387(53 #14137). Zbl 0213.40401.

  2. D.Gaşpar, Spectral ρ-dilation for the representation of function algebras, Anal. Univ. Timişoara, ser. şt. mat. 3 (1970), 153-157. MR0326400(48 #4744). Zbl 0288.46048.

  3. D.Gaşpar, On absolutely continuous representations of function algebras, Rev. Roum. Math. Puret et Appl. XVII, 1 (1972), 21-31. MR0303298(46 #2436). Zbl 0241.46054.

  4. I. Glicksberg, The abstract F. and M. Riesz theorem, J. Functional Anal., 1 (1967),109-122. MR0211264(35 #2146). Zbl 0155.18503.

  5. A. Juratoni and N. Suciu, Spectral ρ- dilations for some representations of uniform algebra, Proceedings of 9th National Conference of the Roumanian Mathematical Society, Ed. Univ. Vest, 194-210.

  6. A. Juratoni, On the weak ρ-spectral representations of function algebras, to appear in Proc. of the 11th Symp. of Math. and Appl.

  7. T. Nakazi, ρ dilations and hypo-Dirichlet algebras, Acta Sci. Math. (Szeged), 56 (1992), 175-181. MR1204751(94b:47010). Zbl 0803.46061.

  8. T. Nakazi, Some special bounded homomorphism of uniform algebras and dilations, Department of Mathematics, Hokkaido University, Sapporo 060, Japan, preprint, 1992, 1-9.

  9. I. Suciu, Function Algebras, Noordhoff Intern. Publ. Leyden}, The Netherlands,1975. MR0370199(51 #6428).

  10. T.P. Srinivasan and Ju-Kwei Wang, Weak* Dirichlet algebras, Function Algebras, Scott, Foresman and Co, 1966, 216-249. MR0198282(33 #6441).

Adina Juratoni
Politehnica University of Timişoara,
Romania.
e-mail: adinajuratoni@yahoo.com

http://www.utgjiu.ro/math/sma