A matricial corona theorem
Authors:
Tavan Trent and Xinjun Zhang
Journal:
Proc. Amer. Math. Soc. 134 (2006), 25492558
MSC (2000):
Primary 32A65, 46J20
Published electronically:
April 7, 2006
MathSciNet review:
2213732
Fulltext PDF Free Access
Abstract 
References 
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Additional Information
Abstract: We show that a usual coronatype theorem on a space of functions automatically extends to a matrix version.
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, An corona theorem on the bidisk for infinitely many functions, submitted.
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 [2]
 L. Carleson, Interpolation by bounded analytic functions and the corona problem, Annals of Math. 76 (1962), 547559. MR 0141789 (25:5186)
 [3]
 S. Fisher, Function Theory on Planar Domains, a Second Course in Complex Analysis, John Wiley and Sons, New York, 1983. MR 0694693 (85d:30001)
 [4]
 F. Forelli, Bounded holomorphic functions and projections, Illinois J. Math. 10 (1966), 367380. MR 0193534 (33:1754)
 [5]
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 [6]
 A. Nicolau, The corona property for bounded analytic functions in some Besov spaces, Proc. Amer. Math. Soc. 110 (1990), 135140. MR 1017007 (90m:46090)
 [7]
 N. K. Nikolski, Treatise on the Shift Operator, SpringerVerlag, New York, 1985. MR 0827223 (87i:47042)
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 M. Rosenblum, A corona theorem for countably many functions, Integral Equa. Oper. Theory 3 (1980), 125137. MR 0570865 (81e:46034)
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 E. L. Stout, Bounded holomorphic functions on finite Riemann surfaces, Trans. Amer. Math. Soc. 120 (1965), 255285. MR 0183882 (32:1358)
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 V. A. Tolokonnikov, Estimates in Carleson's corona theorem and finitely generated ideals in the algebra , Functional Anal. I Prilozhen 14 (1980), 8586 (in Russian). MR 0595742 (82a:46058)
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 [12]
 T. T. Trent, A corona theorem for multipliers on Dirichlet space, Integral Equa. Oper. Theory 49 (2004), 123139. MR 2057771
 [13]
 , A new estimate for the vectorvalued corona problem, J. Func. Anal. 189 (2002), 267282. MR 1887635 (2002m:30067)
 [14]
 , An corona theorem on the bidisk for infinitely many functions, submitted.
 [15]
 X. Zhang, A matrix version of corona theorem for algebras of functions on reproducing kernel Hilbert spaces, Ph.D. dissertation, The University of Alabama, Tuscaloosa, AL, August 2004.
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Additional Information
Tavan Trent
Affiliation:
Department of Mathematics, The University of Alabama, Box 870350, Tuscaloosa, Alabama 354870350
Email:
ttrent@gp.as.ua.edu
Xinjun Zhang
Affiliation:
Department of Mathematics, The University of Alabama, Box 870350, Tuscaloosa, Alabama 354870350
Email:
zhang010@bama.ua.edu
DOI:
http://dx.doi.org/10.1090/S000299390608172X
PII:
S 00029939(06)08172X
Keywords:
Matrix corona theorem
Received by editor(s):
September 8, 2004
Received by editor(s) in revised form:
January 13, 2005
Published electronically:
April 7, 2006
Additional Notes:
This work was partially supported by NSF Grant DMS0400307.
Communicated by:
Joseph A. Ball
Article copyright:
© Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
