A lower bound for the spectral radius

Pták, Vlastimil

doi:10.1090/S0002-9939-1980-0580999-0

A lower bound for the spectral radius
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Proc. Amer. Math. Soc. 80 (1980), 435-440 Request permission

Abstract:

We prove an inequality for a problem of Carathéodory type: given n inner functions ${m_1},{m_2}, \ldots ,{m_n}$, to find the smallest norm of an ${H^\infty }$ function such that the first n terms of its power series coincide with those of the product ${m_1} \cdots {m_n}$. As an application, we obtain a lower bound for the spectral radius of an n-dimensional operator on Hilbert space in terms of its norm and the norm of its nth power.

References

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Ob odnoj teoreme Maříka-Ptáka

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Subgarmoničeskije funkcii na orientirovannom grafe

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