Geodesic
Analytic projections, Corona problem and geometry of holomorphic vector bundles
Treil, Sergei1 ; Wick, Brett2
1 Department of Mathematics, Brown University, 151 Thayer Street, Box 1917, Providence, Rhode Island 02912
2 Department of Mathematics, University of South Carolina, LeConte College, 1523 Greene Street, Columbia, South Carolina 29208
Journal of the American Mathematical Society, Tome 22 (2009) no. 1, pp. 55-76

Voir la notice de l'article provenant de la source American Mathematical Society

The main result of the paper is a theorem giving a sufficient condition for the existence of a bounded analytic projection onto a holomorphic family of generally infinite dimensional subspaces (a holomorphic sub-bundle of a trivial bundle). This sufficient condition is also necessary in the case of finite dimension or codimension of the bundle. A simple lemma of N. Nikolski connects the existence of a bounded analytic projection with the Operator Corona Problem (existence of a bounded analytic left inverse for an operator-valued function), so as corollaries of the main result we obtain new results about the Operator Corona Problem. In particular, we find a new sufficient condition, a complete solution in the case of finite codimension, and a solution of the generalized Corona Problem.
DOI : 10.1090/S0894-0347-08-00611-5

Treil, Sergei 1 ; Wick, Brett 2

1 Department of Mathematics, Brown University, 151 Thayer Street, Box 1917, Providence, Rhode Island 02912
2 Department of Mathematics, University of South Carolina, LeConte College, 1523 Greene Street, Columbia, South Carolina 29208 
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Treil, Sergei; Wick, Brett. Analytic projections, Corona problem and geometry of holomorphic vector bundles. Journal of the American Mathematical Society, Tome 22 (2009) no. 1, pp. 55-76. doi: 10.1090/S0894-0347-08-00611-5

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