# Polynomial as a new variable — A Banach algebra with a functional calculus

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**Polynomial as a new variable — A Banach algebra with a functional calculus.** / Nevanlinna, Olavi.

Research output: Contribution to journal › Article › Scientific › peer-review

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*OPERATORS AND MATRICES*, vol. 10, no. 3, pp. 567-592. https://doi.org/10.7153/oam-10-33

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*OPERATORS AND MATRICES*,

*10*(3), 567-592. https://doi.org/10.7153/oam-10-33

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TY - JOUR

T1 - Polynomial as a new variable — A Banach algebra with a functional calculus

AU - Nevanlinna, Olavi

PY - 2016/9/1

Y1 - 2016/9/1

N2 - Given any square matrix or a bounded operator A in a Hilbert space such that p(A) is normal (or similar to normal), we construct a Banach algebra, depending on the polynomial p, for which a simple functional calculus holds. When the polynomial is of degree d, then the algebra deals with continuous ℂd-valued functions, defined on the spectrum of p(A). In particular, the calculus provides a natural approach to deal with nontrivial Jordan blocks and one does not need differentiability at such eigenvalues.

AB - Given any square matrix or a bounded operator A in a Hilbert space such that p(A) is normal (or similar to normal), we construct a Banach algebra, depending on the polynomial p, for which a simple functional calculus holds. When the polynomial is of degree d, then the algebra deals with continuous ℂd-valued functions, defined on the spectrum of p(A). In particular, the calculus provides a natural approach to deal with nontrivial Jordan blocks and one does not need differentiability at such eigenvalues.

KW - Functional calculus

KW - Multicentric calculus

KW - Polynomially normal

KW - Removing Jordan blocks

KW - Spectral mapping

UR - http://www.scopus.com/inward/record.url?scp=84994052096&partnerID=8YFLogxK

U2 - 10.7153/oam-10-33

DO - 10.7153/oam-10-33

M3 - Article

VL - 10

SP - 567

EP - 592

JO - OPERATORS AND MATRICES

JF - OPERATORS AND MATRICES

SN - 1846-3886

IS - 3

ER -

ID: 9362561