ON AN OPERATOR THEORY APPROACH TO THE CORONA PROBLEM

Autor:	E. Amar, C. Menini
Rok vydání:	2002
Předmět:	Theoretical physics TheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITY General Mathematics Operator theory Mathematics
Zdroj:	Bulletin of the London Mathematical Society. 34:369-373
ISSN:	1469-2120 0024-6093
DOI:	10.1112/s0024609302001029
Popis:	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.
Databáze:	OpenAIRE
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