Estimates for the norm of powers of Volterra's operator through its singular values

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Abstract

We prove that for every Volterra operator T the inequality ∥T2m∥ ≤ b2m (s1(T) · ... · sm(T))2 holds, where b is an absolute constant and s1(T), s2(T), ... are its singular values.

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Dostanić, M. R. (2001). Estimates for the norm of powers of Volterra’s operator through its singular values. Mathematische Zeitschrift, 236(3), 453–459. https://doi.org/10.1007/PL00004837

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