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 -