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A matricial corona theorem II
Author(s):
Tavan
T.
Trent;
Xinjun
Zhang
Journal:
Proc. Amer. Math. Soc.
135
(2007),
2845-2854.
MSC (2000):
Primary 32A65, 46J20
Posted:
May 4, 2007
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Abstract:
We extend the ``matricial corona theorem'' of M. Andersson to general algebras of functions which satisfy a corona theorem.
References:
-
- 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
 , 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
 corona theorem, Pac. J. Math. 104 (2000), 491-509.MR 1760796 (2001j:46075)
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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:
10.1090/S0002-9939-07-08806-5
PII:
S 0002-9939(07)08806-5
Keywords:
Matrix corona theorem
Received by editor(s):
March 9, 2006
Received by editor(s) in revised form:
May 25, 2006
Posted:
May 4, 2007
Additional Notes:
The authors were partially supported by NSF Grant DMS-0400307.
Communicated by:
Joseph A. Ball
Copyright of article:
Copyright
2007,
American Mathematical Society
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