Index Formulas for Toeplitz Operators, Approximate Identities, and the Wolf–Havin Theorem

Chapter
Part of the Operator Theory: Advances and Applications book series (OT, volume 261)

Abstract

This is a review of a development in the 1970s and 1980s that was concerned with index formulas for block Toeplitz operators with discontinuous symbols. We cite the classical results by Douglas and Sarason, outline Silbermann’s approach to index formulas via algebraization, and embark on the replacement of the Abel–Poisson means by arbitrary approximate identities. One question caused by this development was whether the Abel–Poisson means are the only approximative identities that are asymptotically multiplicative on (H,H), and the review closes with Wolf and Havin’s theorem, which gives an affirmative answer to this question.

Keywords

Toeplitz operator index formula approximate identity asymptotic multiplicativity BMO VMO Viktor Havin 

Mathematics Subject Classification (2010)

Primary 47B35. Secondary 30H05 42A10 46J15 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Fakultät für MathematikTechnische Universität ChemnitzChemnitzGermany

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