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Joint mean oscillation and local ideals in the Toeplitz algebra

Author(s): Jingbo Xia
Journal: Proc. Amer. Math. Soc. 128 (2000), 2033-2042.
MSC (1991): Primary 46H10, 47B35, 47C15
Posted: November 23, 1999
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Abstract: We introduce the joint local mean oscillation LMO$(f,g)(\tau )$ and discuss to what extent this function-theoretical quantity serves as a $C^{\ast }$-algebraic invariant in the full Toeplitz algebra ${\mathcal{T}} = {\mathcal{T}}(L^{\infty }).$

References:

[1]
S. Axler, S.-Y. Chang, and D. Sarason, Products of Toeplitz operators, Integral Eq. Operator Theory 1 (1978), 285-309. MR 80d:47039

[2]
R. Douglas, Banach algebra techniques in operator theory, Academic Press, New York, 1972. MR 50:14335

[3]
J. Garnett, Bounded analytic functions, Academic press, New York, 1981. MR 83g:30037

[4]
P. Muhly and J. Xia, Calderon-Zygmund operators, local mean oscillation and certain automorphisms of the Toeplitz algebra, Amer. J. Math. 117 (1995), 1157-1201. MR 96k:47045

[5]
D. Sarason, Functions of vanishing mean oscillation, Trans. Amer. Math. Soc. 207 (1975), 391-405. MR 51:13690

[6]
D. Sarason, Products of Toeplitz operators, Lecture Notes in Mathematics Vol. 1573, Springer-Verlag, Berlin, 1994.

[7]
A. Volberg, Two remarks concerning the theorem of S. Axler, S.-Y. A. Chang, and D. Sarason, J. Operator Theory 8 (1982), 209-218. MR 84h:47038a

[8]
D. Xia and D. Zheng, Products of Hankel operators, Integral Eq. Operator Theory 29 (1997), 339-363. CMP 98:03

[9]
J. Xia, Rigged non-tangential maximal functions associated with Toeplitz operators and Hankel operators, Pacific J. Math. 182 (1998), 385-396. CMP 98:09

[10]
D. Zheng, The distribution function inequality and products of Toeplitz operators and Hankel operators, J. Funct. Anal. 138 (1996), 477-501. MR 97e:47040

[11]
D. Zheng, Toeplitz operators and Hankel operators on the Hardy space of the unit sphere, J. Funct. Anal. 149 (1997), 1-24. MR 98m:47038

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Additional Information:

Jingbo Xia
Affiliation: Department of Mathematics, State University of New York at Buffalo, Buffalo, New York 14214
Email: jxia@acsu.buffalo.edu

DOI: 10.1090/S0002-9939-99-05369-1
PII: S 0002-9939(99)05369-1
Received by editor(s): August 24, 1998
Posted: November 23, 1999
Additional Notes: This research was supported in part by National Science Foundation grant DMS-9703515.
Communicated by: David R. Larson
Copyright of article: Copyright 2000, American Mathematical Society

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