If a bounded operator A matches a normal operator N in the norm of every polynomial p(A), p(N), then A is normal in the finite-dimensional case and for compact (c,p)-norm case; for the operator norm, this holds exactly when the spectrum of N is a Lavrentieff set.
Title resolution pending
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
fields
math.FA 1years
2019 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Operators which are polynomially isometric to a normal operator
If a bounded operator A matches a normal operator N in the norm of every polynomial p(A), p(N), then A is normal in the finite-dimensional case and for compact (c,p)-norm case; for the operator norm, this holds exactly when the spectrum of N is a Lavrentieff set.