On the norm of polynomials of two adjoint projections

Israel Feldman; Naum Krupnik; Alexander Markus

doi:10.1007/BF01194927

On the norm of polynomials of two adjoint projections

Israel Feldman, Naum Krupnik, Alexander Markus

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

25 Scopus citations

Abstract

Let f(X, Y) be a polynomial of two non-commuting variables and let P be an arbitrary nontrivial projection operator in Hilbert space. The class of all polynomials f(X, Y) for which {norm of matrix}f(P, P^*){norm of matrix} depends only on f and {norm of matrix}P{norm of matrix} are described. In the case when such a dependence exists the explicit formula is obtained. Some applications to singular integral operators are given.

Original language	English
Pages (from-to)	69-91
Number of pages	23
Journal	Integral Equations and Operator Theory
Volume	14
Issue number	1
DOIs	https://doi.org/10.1007/BF01194927
State	Published - 1 Jan 1991

ASJC Scopus subject areas

Analysis
Algebra and Number Theory

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10.1007/BF01194927

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AB - Let f(X, Y) be a polynomial of two non-commuting variables and let P be an arbitrary nontrivial projection operator in Hilbert space. The class of all polynomials f(X, Y) for which {norm of matrix}f(P, P*){norm of matrix} depends only on f and {norm of matrix}P{norm of matrix} are described. In the case when such a dependence exists the explicit formula is obtained. Some applications to singular integral operators are given.

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On the norm of polynomials of two adjoint projections

Abstract

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