A matricial corona theorem II
HTML articles powered by AMS MathViewer
- by Tavan T. Trent and Xinjun Zhang
- Proc. Amer. Math. Soc. 135 (2007), 2845-2854
- DOI: https://doi.org/10.1090/S0002-9939-07-08806-5
- Published electronically: May 4, 2007
- PDF | Request permission
Abstract:
We extend the “matricial corona theorem” of M. Andersson to general algebras of functions which satisfy a corona theorem.References
- Mats Andersson, The corona theorem for matrices, Math. Z. 201 (1989), no. 1, 121–130. MR 990193, DOI 10.1007/BF01161999
- N. K. Nikol′skiĭ, Treatise on the shift operator, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 273, Springer-Verlag, Berlin, 1986. Spectral function theory; With an appendix by S. V. Hruščev [S. V. Khrushchëv] and V. V. Peller; Translated from the Russian by Jaak Peetre. MR 827223, DOI 10.1007/978-3-642-70151-1
- A. Sasane, Irrational transfer function classes, coprime factorization and stabilization, CDAM Research Report CDAM-LSE-2005-10.
- —, An operator corona theorem for a class of subspaces of $H^{\infty }$, preprint.
- S. R. Treil′, Angles between co-invariant subspaces, and the operator corona problem. The Szőkefalvi-Nagy problem, Dokl. Akad. Nauk SSSR 302 (1988), no. 5, 1063–1068 (Russian); English transl., Soviet Math. Dokl. 38 (1989), no. 2, 394–399. MR 981054
- Tavan T. Trent, A corona theorem for multipliers on Dirichlet space, Integral Equations Operator Theory 49 (2004), no. 1, 123–139. MR 2057771, DOI 10.1007/s00020-002-1196-6
- Tavan Trent and Xinjun Zhang, A matricial corona theorem, Proc. Amer. Math. Soc. 134 (2006), no. 9, 2549–2558. MR 2213732, DOI 10.1090/S0002-9939-06-08172-X
- Jie Xiao, The $Q_p$ corona theorem, Pacific J. Math. 194 (2000), no. 2, 491–509. MR 1760796, DOI 10.2140/pjm.2000.194.491
Bibliographic Information
- Tavan T. Trent
- Affiliation: Department of Mathematics, The University of Alabama, Box 870350, Tuscaloosa, Alabama 35487-0350
- Email: ttrent@gp.as.ua.edu
- Xinjun Zhang
- Affiliation: Department of Mathematics, University of Wisconsin-Baraboo, Baraboo, Wisconsin 53913
- Email: szhang@uwc.edu
- Received by editor(s): March 9, 2006
- Received by editor(s) in revised form: May 25, 2006
- Published electronically: May 4, 2007
- Additional Notes: The authors were partially supported by NSF Grant DMS-0400307.
- Communicated by: Joseph A. Ball
- © Copyright 2007 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 135 (2007), 2845-2854
- MSC (2000): Primary 32A65, 46J20
- DOI: https://doi.org/10.1090/S0002-9939-07-08806-5
- MathSciNet review: 2317961