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- W2011485491 abstract "It is known that the algebra of Schur operators on ℓ 2 (namely operators bounded on both ℓ 1 and ℓ ∞ ) is not inverse-closed. When ℓ 2 = ℓ 2 ( X ) where X is a metric space, one can consider elements of the Schur algebra with certain decay at infinity. For instance if X has the doubling property, then Q. Sun has proved that the weighted Schur algebra A ω ( X ) for a strictly polynomial weight ω is inverse-closed. In this paper, we prove a sharp result on left-invertibility of the these operators. Namely, if an operator A ∈ A ω ( X ) satisfies ‖ A f ‖ p ≽ ‖ f ‖ p , for some 1 ⩽ p ⩽ ∞ , then it admits a left-inverse in A ω ( X ) . The main difficulty here is to obtain the above inequality in ℓ 2 . The author was both motivated and inspired by a previous work of Aldroubi, Baskarov and Krishtal (2008) [1] , where similar results were obtained through different methods for X = Z d , under additional conditions on the decay." @default.
- W2011485491 created "2016-06-24" @default.
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- W2011485491 date "2010-12-01" @default.
- W2011485491 modified "2023-09-28" @default.
- W2011485491 title "Left inverses of matrices with polynomial decay" @default.
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- W2011485491 doi "https://doi.org/10.1016/j.jfa.2010.07.014" @default.
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