Feynman's operational calculi: spectral theory for noncommuting self-adjoint operators
type: Item
instance of: scholarly article
title: Feynman's operational calculi: spectral theory for noncommuting self-adjoint operators
zbMATH Open document ID: 1180.47013
author: G. W. Johnson
author: Lance Nielsen
author: Brian Jefferies
published in: Mathematical Physics, Analysis and Geometry
publication date: 2009-05-22T00:00:00Z
review text: Let \((A_1,\dots,A_n)\) be an \(n\)-tuple of linear bounded operators acting on a Banach space \(X\). The continuous probability measures \(\mu_1,\dots,\mu_n\), defined on the Borel class of \([0,1]\), determine an operational calculus from a commutative Banach algebra \(\mathbb{D}(A_1,\dots,A_n)\) (the disentangling algebra of analytic functions) into the Banach algebra \(L(X)\) of all the operators on \(X\). In this paper, it is proved the following result: an \(n\)-tuple \((A_1,\dots,A_n)\) of bounded selfadjoint operators on a Hilbert space \(H\) is of Paley-Wiener type \((0,r,\mu)\), with \(r=(\|A_1\|^2 + \cdots + \|A_n\|^2)^{1/2}\), for any \(n\)-tuple \(\mu_1,\dots,\mu_n\), a property related with the above functional calculus.
reviewed by: Antonio Martinón
Mathematics Subject Classification ID: 47A60
Mathematics Subject Classification ID: 46J15
zbMATH DE Number: 5556069
MaRDI profile type: Publication
full work available at URL: s11040-007-9021-8
OpenAlex ID: W1970458680
cites work: Q3995021
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DOI: 10.1007/S11040-007-9021-8
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description: scientific article; zbMATH DE number 5556069