Preservers of local spectrum of matrix skew products

Abstract

Let be the space of complex matrices, and for a nonzero vector and , let denote the local spectrum of T at e. Characterizations are obtained for maps on satisfying

where the binary operation stands for the skew Jordan semi-triple product or the skew product on matrices, with no additional assumption on the range of the map .

Keywords:

• Local spectrum
• single-valued extension property
• Jordan products
• nonlinear preservers

AMS Subject Classifications:

• 47B49
• 47A10
• 47A11

Acknowledgements

The author is greatly indebted to the editor and the referee for many valuable comments and suggestions which improved the initial draft of this paper.

Notes

No potential conflict of interest was reported by the author.

Additional information

Funding

This work was partially supported by a grant from MIU-SRA, Morocco.