Convexity of ranges and connectedness of level sets of quadratic forms

I. Feldman, N. Krupnik, A. Markus

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

O. Toeplitz and F. Hausdorff proved that the range of any quadratic form on the unit sphere S of an inner product space X is convex and the level sets of any Hermitian form on S are connected. We consider the question: Which subsets of X, besides S, have these properties?

Original languageEnglish
Title of host publicationCharacteristic Functions, Scattering Functions and Transfer Functions
EditorsDaniel Alpay, Victor Vinnikov
PublisherSpringer International Publishing
Pages149-179
Number of pages31
ISBN (Print)9783034601825
DOIs
StatePublished - 1 Jan 2010
EventInternational Conference on Characteristic functions and transfer functions in operator theory and system theory, 2007 - Beersheba, Israel
Duration: 9 Jul 200713 Jul 2007

Publication series

NameOperator Theory: Advances and Applications
Volume197
ISSN (Print)0255-0156
ISSN (Electronic)2296-4878

Conference

ConferenceInternational Conference on Characteristic functions and transfer functions in operator theory and system theory, 2007
Country/TerritoryIsrael
CityBeersheba
Period9/07/0713/07/07

Keywords

  • Connectedness
  • Convexity
  • Numerical range
  • Quadratic forms
  • Toeplitz-Hausdorff Theorem

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