A maximum principle for quotient norms in $H^ \infty$
Author:
Eric Hayashi
Journal:
Proc. Amer. Math. Soc. 99 (1987), 323-327
MSC:
Primary 30E10; Secondary 30C15, 30D50
DOI:
https://doi.org/10.1090/S0002-9939-1987-0870794-3
MathSciNet review:
870794
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Abstract | References | Similar Articles | Additional Information
Abstract: Let $G$ be a closed subset of the open unit disk $D$ in the complex plane, and let $p$ denote a general polynomial of degree $n$ which has all of its roots in $G$. For a fixed $h$ in ${H^\infty },||h - p{H^\infty }|{|_{{H^\infty }/p{H^\infty }}}$ is maximized only if all the zeros of $p$ are on the boundary of $G$.
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- Vlastimil Pták and N. J. Young, Functions of operators and the spectral radius, Linear Algebra Appl. 29 (1980), 357–392. MR 562769, DOI https://doi.org/10.1016/0024-3795%2880%2990250-5
- Donald Sarason, Operator-theoretic aspects of the Nevanlinna-Pick interpolation problem, Operators and function theory (Lancaster, 1984) NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., vol. 153, Reidel, Dordrecht, 1985, pp. 279–314. MR 810449
- N. J. Young, A maximum principle for interpolation in $H^{\infty }$, Acta Sci. Math. (Szeged) 43 (1981), no. 1-2, 147–152. MR 621366 ---, Maximum principles for quotient norms in ${H^\infty }$, Lecture Notes in Math., vol. 1043, Springer-Verlag, Berlin and New York, 1984, pp. 53-54.
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Article copyright:
© Copyright 1987
American Mathematical Society
