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Acta mathematica scientia,Series A ›› 2008, Vol. 28 ›› Issue (6): 1181-1186.

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Functional Representation Theorem for Polynomially Bounded Operators on a Banach Space

Liu Mingxue

(Department of Mathematics, Guangdong Polytechnic Normal University, Guangzhou 510665)

Received:2006-09-12 Revised:2007-12-19 Online:2008-12-25 Published:2008-12-25
Contact: Liu Mingxue

Abstract

Abstract:

In this paper, the author introduces a transformation by scalar multiplication
of the independent variable in the disc algebra, finds the connection between the Riesz functional calculus of polynomially bounded operators and the polynomial calculus of polynomially bounded operators, and obtains the functional representation theorem for (general) polynomially bounded operators on a Banach space.

Key words: Banach space, Polynomially bounded operator, Functional calculus, Invariant subspace

CLC Number:

47B40

Liu Mingxue. Functional Representation Theorem for Polynomially Bounded Operators on a Banach Space[J].Acta mathematica scientia,Series A, 2008, 28(6): 1181-1186.

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Functional Representation Theorem for Polynomially Bounded Operators on a Banach Space

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