Abstract
For the Frobenius matrix accompanying an algebraic (differential) equation in a complex Banach algebra, the Cayley–Hamilton theorem is proved, which is used to obtain a representation of the resolvent.
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Acknowledgments
The author is grateful to Professor A. N. Perov for scientific supervision and valuable comments, which helped to substantially improve the paper.
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This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.
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Translated from Funktsional'nyi Analiz i ego Prilozheniya, 2023, Vol. 57, pp. 130–132 https://doi.org/10.4213/faa4093.
Dedicated to the 110th birthday of Izrael Moiseevich Gel’fand
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Kostrub, I.D. The Cayley–Hamilton Theorem and Resolvent Representation. Funct Anal Its Appl 57, 371–373 (2023). https://doi.org/10.1134/S001626632304010X
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DOI: https://doi.org/10.1134/S001626632304010X