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Abstract. For bounded symmetric domains f2 c CN, a bilaterial shift operator U is shown to exist on the Bergman space A2(Q) such that UTj — TfU is a compact operator for all Toeplitz operators 7/y. This may be viewed as an extension of the well-known fact that S * TS- T- 0 whenever T is a Toeplitz operator on H2, S being the unilateral shift. It also follows that the C*-algebra generated by Toeplitz operators on A2{Q) does not contain all bounded operators. Let fi be a bounded symmetric (Cartan) domain with its standard (Harish-Chandra) realization in C ^ [6], dv the 2«-dimensional Lebesgue measure on fi, and L2(fi, dv) the Hilbert space of square-integrable complex-valued functions on fi. The Bergman space, A2(Q), is the closed subspace of 72(Q, dv) consisting of functions analytic on fi. Denote by P the orthogonal projectio

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0002-9939/93 $1.00 + $.25 per page

Year: 2013

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oai:CiteSeerX.psu:10.1.1.352.2646

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