The essential norm of operators in the Toeplitz algebra on $A^p(B_n)$

By Daniel Suarez. 2007

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for 1 < p < oo, and T p be the corresponding Toeplitz algebra. We show that every S ∈ Sp can be approximated by operators that are specially suited for the study of local behavior. This is used to obtain several estimates for the essential norm of S ∈ Sp, an estimate for the essential spectral radius of S ∈ T 2 , and a localization result for its essential spectrum. Finally, we characterize compactness in terms of the Berezin transform for operators in T p .

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

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