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Operators with a given part of the numerical range

  • Janko Bračič EMAIL logo and Cristina Diogo EMAIL logo
Published/Copyright: April 30, 2016
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 66 Issue 1

Abstract

Sets of operators which have a given set of numbers in the numerical range are studied. We prove an interesting result which characterizes the set of operators that have 0 in the convex hull of its spectrum. Along the way we give a simpler proof of the well known Hilbebrandt’s theorem.

Keywords: numerical range; Hildebrandt’s theorem
MSC: Primary 47A12

The work was partially supported by FCT through the Program POCI 2010/FEDER and the project PTDC/MAT/121837/2010, Portugal.

  1. This paper has been communicated by Michal Zajac

Acknowledgement

We would like to thank the referee for valuable comments and suggestions.

References

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Received: 2013-3-27
Accepted: 2013-6-7
Published Online: 2016-4-30
Published in Print: 2016-2-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2015-0134
Keywords for this article
numerical range; Hildebrandt’s theorem

Articles in the same Issue

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  2. Prof. RNDr. Ján Jakubík, DrSc. passed away
  3. Research Article
  4. On the number of slim, semimodular lattices
  5. Research Article
  6. Quantum computational algebra with a non-commutative generalization
  7. Research Article
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  9. Research Article
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  11. Research Article
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  13. Research Article
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  15. Research Article
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  17. Research Article
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