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ON AN OPERATOR THEORY APPROACH TO THE CORONA PROBLEM

Published online by Cambridge University Press:  22 May 2002

E. AMAR  and
C. MENINI
E. AMAR
Affiliation:
Université de Bordeaux I, M.P.B., 351 Cours de la Libération, 33405 Talence, [email protected]@math.u-bordeaux.fr
C. MENINI
Affiliation:
Université de Bordeaux I, M.P.B., 351 Cours de la Libération, 33405 Talence, [email protected]@math.u-bordeaux.fr
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Abstract

This paper deals with an operator theory approach to the corona conjecture for H∞([ ]n). Treil gave a counter-example to this conjecture in the case where n = 1 for operator-valued functions; thus one might hope to use this to disprove the corona conjecture for H∞([ ]n) (for n [ges ] 2). This paper shows that this natural approach towards a negative answer fails. On the other hand, the second result here shows that ‘commutant lifting’ cannot be true for more than two contractions for any constant. This obstructs a natural attempted proof of the corona conjecture for H∞([ ]n) (for n [ges ] 2) by our previous result.

Type
PAPERS
Information
Bulletin of the London Mathematical Society , Volume 34 , Issue 3 , May 2002 , pp. 369 - 373
Copyright
© The London Mathematical Society 2002

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