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.
In memory of Viktor Petrovich Havin
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Böttcher, A. (2018). Index Formulas for Toeplitz Operators, Approximate Identities, and the Wolf–Havin Theorem. In: Baranov, A., Kisliakov, S., Nikolski, N. (eds) 50 Years with Hardy Spaces. Operator Theory: Advances and Applications, vol 261. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-59078-3_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-59078-3_8
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-59077-6
Online ISBN: 978-3-319-59078-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)