Estimates for Elements of Inverse Matrices for a Class of Operators with Matrices of Special Structure |
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Authors: | Azarnova T V |
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Institution: | (1) Voronezh State University, Russia |
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Abstract: | 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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Keywords: | inverse matrix linear bounded operator in Banach space Fourier analysis of strongly continuous periodic functions |
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