论文标题
通过多项式简化操作员
Simplifying operators by polynomials
论文作者
论文摘要
我们收集并组织已知结果并添加以下性质的一些新结果：如果A是Hilbert或Banach空间中的有界操作员，是否存在非恒定的多项式P（Z），使P（A）是“更简单”的，“更简单”。 Suppose a particular functional calculus is applicable to p(A) but not directly to A. Using "multicentric calculus" one can represent functions using p(z) as a new variable allowing the functional calculus to be extended to apply to A. Classes of operators considered are increasing chains like finite rank, compact , Riesz, almost algebraic, quasialgebraic, biquasitriangular, quasitriangular,有限。
We collect and organise known results and add some new ones of the following nature: if A is a bounded operator in a Hilbert or Banach space, does there exist a nonconstant polynomial p(z) such that p(A) is "simpler", "nicer" than A. The motivation for organising these is the following. Suppose a particular functional calculus is applicable to p(A) but not directly to A. Using "multicentric calculus" one can represent functions using p(z) as a new variable allowing the functional calculus to be extended to apply to A. Classes of operators considered are increasing chains like finite rank, compact , Riesz, almost algebraic, quasialgebraic, biquasitriangular, quasitriangular, bounded.
