A note on the Fredholm properties of Toeplitz operators on weighted Bergman spaces with matrix-valued symbolsPerälä, A. and Virtanen, J. A. (2011) A note on the Fredholm properties of Toeplitz operators on weighted Bergman spaces with matrix-valued symbols. Operators and Matrices, 5 (1). pp. 97-106. ISSN 1846-3886 Full text not archived in this repository. It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing. To link to this item DOI: 10.7153/oam-05-06 Abstract/SummaryWe characterize the essential spectra of Toeplitz operators Ta on weighted Bergman spaces with matrix-valued symbols; in particular we deal with two classes of symbols, the Douglas algebra C+H∞ and the Zhu class Q := L∞ ∩VMO∂ . In addition, for symbols in C+H∞ , we derive a formula for the index of Ta in terms of its symbol a in the scalar-valued case, while in the matrix-valued case we indicate that the standard reduction to the scalar-valued case fails to work analogously to the Hardy space case. Mathematics subject classification (2010): 47B35,
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