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derivative of the norm of a linear mapping; linear differential equations in a Banach space; normed space; solution of the differential equation

References:

[1] A. N. Kolmogorov S. V. Fomin: **Foundations of the theory of functions and functional analysis**. (Russian). Czech translation, Praha, 1975.

[2] J. Dieudonné: **Foundations of modern analysis**. Academic Press, New York-London, 1960; Russian translation, Mir, Moscow. MR 0120319