Abstract
We obtain a necessary and sufficient condition for the norm of the exponential of a linear operator on a Banach space not to exceed the exponential of its spectral radius. The condition is stated in terms of the logarithmic norm of the original operator.
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References
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Original Russian Text © A.I. Perov, 2017, published in Differentsial’nye Uravneniya, 2017, Vol. 53, No. 3, pp. 438–440.
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Perov, A.I. An estimate of the norm of the Cauchy operator for linear differential equations. Diff Equat 53, 429–432 (2017). https://doi.org/10.1134/S0012266117030132
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DOI: https://doi.org/10.1134/S0012266117030132