Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A matricial corona theorem II


Authors: Tavan T. Trent and Xinjun Zhang
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
Published electronically: May 4, 2007
MathSciNet review: 2317961
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We extend the ``matricial corona theorem'' of M. Andersson to general algebras of functions which satisfy a corona theorem.


References [Enhancements On Off] (What's this?)

  • 1. M. Andersson, The corona theorem for matrices, Math. Z. 201 (1989), 121-130.MR 0990193 (90g:30036)
  • 2. N. K. Nikolski, Treatise on the Shift Operator, Springer-Verlag, New York, 1985.MR 0827223 (87i:47042)
  • 3. A. Sasane, Irrational transfer function classes, coprime factorization and stabilization, CDAM Research Report CDAM-LSE-2005-10.
  • 4. -, An operator corona theorem for a class of subspaces of $ H^{\infty}$, preprint.
  • 5. S. R. Treil, Angles between coinvariant subspaces and an operator-valued corona problem, a question of Szökefalvi-Nagy, Soviet Math. Dokl. 38 (1989), 394-399. MR 0981054 (90b:47057)
  • 6. T. T. Trent, A corona theorem for multipliers on Dirichlet space, Integral Equa. Oper. Theory 49 (2004), 123-139. MR 2057771 (2005e:30090)
  • 7. T. Trent and X. Zhang, A matricial corona theorem, Proc. Amer. Math. Soc. 134 (2006), 2549-2558.MR 2213732
  • 8. J. Xiao, The $ Q_p$ corona theorem, Pac. J. Math. 104 (2000), 491-509.MR 1760796 (2001j:46075)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 32A65, 46J20

Retrieve articles in all journals with MSC (2000): 32A65, 46J20


Additional 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

DOI: https://doi.org/10.1090/S0002-9939-07-08806-5
Keywords: Matrix corona theorem
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
Article copyright: © Copyright 2007 American Mathematical Society

American Mathematical Society