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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A lower bound for the spectral radius


Author: Vlastimil Pták
Journal: Proc. Amer. Math. Soc. 80 (1980), 435-440
MSC: Primary 15A60; Secondary 30D50
DOI: https://doi.org/10.1090/S0002-9939-1980-0580999-0
MathSciNet review: 580999
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1980-0580999-0
Keywords: Inner functions, $ {H^\infty }$, spectral radius, norms of operators, convergence of iterative processes
Article copyright: © Copyright 1980 American Mathematical Society