Journal of Operator Theory
Volume 76, Issue 1, Summer 2016 pp. 107-131.
Toeplitz operators and Toeplitz algebra with symbols of vanishing oscillation
Authors:
Jingbo Xia (1) and Dechao Zheng (2)
Author institution: (1) Department of Mathematics,
State University of New York at Buffalo,
Buffalo, NY 14260, U.S.A.
(2) Center of Mathematics, Chongqing University,\break
Chongqing, 401331, P.R. China
\textit{and}
Department of Mathematics, Vanderbilt University,
Nashville, TN 37240, U.S.A.
Summary: We study the $C^\ast $-algebra generated by Toeplitz operators with symbols
of vanishing (mean) oscillation on the Bergman space of the unit ball. We show that the index calculation
for Fredholm operators in this $C^\ast $-algebra can be easily and completely reduced to the classic case of
Toeplitz operators with symbols that are continuous on the closed unit ball.
Moreover, in addition to a number of other properties, we show that
this $C^\ast $-algebra has uncountably many Fredholm components.
DOI: http://dx.doi.org/10.7900/jot.2015sep09.2097
Keywords: Fredholm index, Toeplitz algebra, vanishing oscillation
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