Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-30T19:31:55.738Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)