Geodesic
Estimates for Elements of Inverse Matrices for a Class of Operators with Matrices of Special Structure
Matematičeskie zametki, Tome 72 (2002) no. 1, pp. 3-10.

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In this paper, we consider questions related to the structure of inverse matrices of linear bounded operators acting in infinite-dimensional complex Banach spaces. We obtain specific estimates of elements of inverse matrices for bounded operators whose matrices have a special structure. Matrices are introduced as special operator-valued functions on an index set. The matrix structure is described by the behavior of the given function on elements of a special partition of the index set. The method used for deriving the estimates is based on an analysis of Fourier series of strongly continuous periodic functions. 
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T. V. Azarnova. Estimates for Elements of Inverse Matrices for a Class of Operators with Matrices of Special Structure. Matematičeskie zametki, Tome 72 (2002) no. 1, pp. 3-10. http://geodesic.mathdoc.fr/item/MZM_2002_72_1_a0/

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