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.

julkaisussa: OPERATORS AND MATRICES, Vuosikerta 10, Nro 3, 01.09.2016, s. 567-592.

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Bibtex - Lataa

@article{5f39a452c846459c8b32e48ec53e57e4,
title = "Polynomial as a new variable — A Banach algebra with a functional calculus",
abstract = "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.",
keywords = "Functional calculus, Multicentric calculus, Polynomially normal, Removing Jordan blocks, Spectral mapping",
author = "Olavi Nevanlinna",
year = "2016",
month = "9",
day = "1",
doi = "10.7153/oam-10-33",
language = "English",
volume = "10",
pages = "567--592",
journal = "OPERATORS AND MATRICES",
issn = "1846-3886",
publisher = "Element d.o.o.",
number = "3",

}

RIS - Lataa

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