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Articles

Continuous selections of the inverse numerical range map

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Pages 87-99 | Received 30 Jan 2015, Accepted 16 Apr 2015, Published online: 15 May 2015
 

Abstract

For a complex -by- matrix , the numerical range is the range of the map acting on the unit sphere in . We ask whether the multivalued inverse numerical range map has a continuous single-valued selection defined on all or part of . We show that for a large class of matrices, does have a continuous selection on . For other matrices, has a continuous selection defined everywhere on except in the vicinity of a finite number of exceptional points on the boundary of .

AMS Subject Classifications:

Acknowledgements

We would like to thank Ilya Spitkovsky for his helpful advice and expertise. Thanks also to Charles Johnson for organizing the summer REU during which this project was started.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by NSF [grant number DMS-0751964].

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