Representation of Suslin sets by operators
type: Item
instance of: scholarly article
title: Representation of Suslin sets by operators
zbMATH Open document ID: 0579.47001
DOI: 10.1007/BF01195868
published in: Integral Equations and Operator Theory
publication date: 1984-01-01T00:00:00Z
review text: The main result is the following: Let \({\mathcal S}\) be a bounded Suslin set in the plane. There is a bounded linear operator T in E, whose point spectrum \(\sigma_ e(T)\) is \({\mathcal S}\). Furthermore the operator T can be chosen from a fixed collection that is \(\sigma\)-compact in the operator norm. In fact, the Banach space is a space of functionals on \(C^ 1_ c({\mathbb{R}})\), not dependent on \({\mathcal S}\). The operator is multiplication by a Hölder-continuous function with exponent 1/3.
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 46F05
zbMATH DE Number: 3927683
zbMATH Keywords: spaces of distributions
zbMATH Keywords: bounded Suslin set in the plane
zbMATH Keywords: bounded linear operator
zbMATH Keywords: point spectrum
zbMATH Keywords: multiplication by a Hölder-continuous function with exponent 1/3
author: Robert Kaufman
reviewed by: Jürgen Voigt
MaRDI profile type: Publication
cites work: Lipschitz spaces and Suslin sets
description: scientific article; zbMATH DE number 3927683