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On an Operator Theory Approach to the Corona Problem
Author(s) -
Amar E.,
Menini C.
Publication year - 2002
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609302001029
Subject(s) - conjecture , mathematics , centralizer and normalizer , operator (biology) , corona (planetary geology) , constant (computer programming) , pure mathematics , combinatorics , discrete mathematics , calculus (dental) , physics , computer science , medicine , biochemistry , chemistry , dentistry , repressor , astrobiology , transcription factor , venus , gene , programming language
This paper deals with an operator theory approach to the corona conjecture for H ∞ (D 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 ∞ (D n ) (for n ⩾ 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 ∞ (D n ) (for n ⩾ 2) by our previous result.