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. 
@article{MZM_2002_72_1_a0,
     author = {T. V. Azarnova},
     title = {Estimates for {Elements} of {Inverse} {Matrices} for a {Class} of {Operators} with {Matrices} of {Special} {Structure}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {3--10},
     publisher = {mathdoc},
     volume = {72},
     number = {1},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2002_72_1_a0/}
}
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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/