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Bracic, J. & Diogo, C. (2017). Simultaneous zero inclusion property for spatial numerical ranges. Journal of Mathematical Analysis and Applications. 449 (2), 1413-1423

J. Bracic and C. I. Diogo,  "Simultaneous zero inclusion property for spatial numerical ranges", in Journal of Mathematical Analysis and Applications, vol. 449, no. 2, pp. 1413-1423, 2017

@article{bracic2017_1713979157946,
	author = "Bracic, J. and Diogo, C.",
	title = "Simultaneous zero inclusion property for spatial numerical ranges",
	journal = "Journal of Mathematical Analysis and Applications",
	year = "2017",
	volume = "449",
	number = "2",
	doi = "10.1016/j.jmaa.2017.01.001",
	pages = "1413-1423",
	url = "http://www.sciencedirect.com/science/article/pii/S0022247X17300124"
}

TY  - JOUR
TI  - Simultaneous zero inclusion property for spatial numerical ranges
T2  - Journal of Mathematical Analysis and Applications
VL  - 449
IS  - 2
AU  - Bracic, J.
AU  - Diogo, C.
PY  - 2017
SP  - 1413-1423
SN  - 0022-247X
DO  - 10.1016/j.jmaa.2017.01.001
UR  - http://www.sciencedirect.com/science/article/pii/S0022247X17300124
AB  - 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.
ER  -