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- W2013200001 abstract "The curvature 𝒦T(w) of a contraction T in the Cowen–Douglas class B1(𝔻) is bounded above by the curvature 𝒦S*(w) of the backward shift operator. However, in general, an operator satisfying the curvature inequality need not be contractive. In this paper, we characterize a slightly smaller class of contractions using a stronger form of the curvature inequality. Along the way, we find conditions on the metric of the holomorphic Hermitian vector bundle ET corresponding to the operator T in the Cowen–Douglas class B1(𝔻) which ensures negative definiteness of the curvature function. We obtain a generalization for commuting tuples of operators in the class B1(Ω) for a bounded domain Ω in ℂm." @default.
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- W2013200001 date "2013-09-29" @default.
- W2013200001 modified "2023-10-16" @default.
- W2013200001 title "Infinitely divisible metrics and curvature inequalities for operators in the Cowen-Douglas class" @default.
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- W2013200001 doi "https://doi.org/10.1112/jlms/jdt045" @default.
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