Artigo em revista científica Q1
Simultaneous zero inclusion property for spatial numerical ranges
Janko Bracic (Bracic, J.); Cristina Diogo (Diogo, C.);
Título Revista
Journal of Mathematical Analysis and Applications
Ano
2017
Língua
Inglês
País
Estados Unidos da América
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Abstract/Resumo
For a finite dimensional complex normed space X, we say that it has the simultaneous zero inclusion property if an invertible linear operator S on X has zero in its spatial numerical range if and only if zero is in the spatial numerical range of the inverse S-1, as well. We show that beside Hilbert spaces there are some other normed spaces with this property. On the other hand, space l(1) (n) does not have this property. Since not every normed space has the simultaneous zero inclusion property, we explore the class of invertible operators at which this property holds. In the end, we consider a property which is stronger than the simultaneous zero inclusion property and is related to the question when it is possible, for every invertible operator S, to control the distance of 0 to the spatial numerical range of S-1 by the distance of 0 to the spatial numerical range of S.
Agradecimentos/Acknowledgements
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Palavras-chave
Spatial numerical range
  • Matemáticas - Ciências Naturais
Registos de financiamentos
Referência de financiamento Entidade Financiadora
UID/MAT/04459/2013 Fundação para a Ciência e a Tecnologia
P2-0268 Slovenian Research Agency