A COLLECTION OF LOCAL SPECTRA PRESERVING MAPS

Document Type : Original Article

Authors
Rohollah Parvinianzadeh 1
Jumakhan Pazhman 2
1 Department of Mathematics, University of Yasouj, Yasouj, Iran.
2 Department of Mathematics, Ghor Institute of higher education, Afghanistan.
10.22034/maco.3.1.6
Abstract
We collected some results about maps on the algebra of all bounded operators that preserve the local spectrum and local spectral radius at nonzero vectors. Also, we describe maps that preserve operators of local spectral radius zero at points and discuss several problems in this direction. Finally, we collect maps that preserve the local spectral subspace of operators associated with any singleton.

Keywords

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Mathematical Analysis and Convex Optimization
Volume 3, Issue 1
June 2022
Pages 49-60