@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",
}