Polynomial as a new variable — A Banach algebra with a functional calculus
Research output: Contribution to journal › Article › Scientific › peer-review
|Number of pages||26|
|Journal||OPERATORS AND MATRICES|
|Publication status||Published - 1 Sep 2016|
|MoE publication type||A1 Journal article-refereed|
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.
- Functional calculus, Multicentric calculus, Polynomially normal, Removing Jordan blocks, Spectral mapping