General preservers of invariant subspace lattices

Gregor Dolinar,Shuanping Du,Jinchuan Hou,Peter Legiša

doi:10.1016/j.laa.2008.02.007

General preservers of invariant subspace lattices

Gregor Dolinar, Shuanping Du + Show 2 more

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https://doi.org/10.1016/j.laa.2008.02.007

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Journal: Linear Algebra and its Applications	Publication Date: Mar 20, 2008
Citations: 17	License type: publisher-specific-oa

Affiliation: Xiamen University, Shanxi Normal University, Taiyuan University of Technology, University of Ljubljana

#Lattice Of Subspaces #Banach Space + Show 4 more

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Abstract

Let B ( X ) be the space of all bounded linear operators on a Banach space X and let Lat A be the lattice of invariant subspaces of the operator A ∈ B ( X ) . We characterize some maps Φ : B ( X ) → B ( X ) with one of the following preserving properties: Lat ( Φ ( A ) + Φ ( B ) ) = Lat ( A + B ) , or Lat ( Φ ( A ) Φ ( B ) ) = Lat ( AB ) , or Lat ( Φ ( A ) Φ ( B ) + Φ ( B ) Φ ( A ) ) = Lat ( AB + BA ) , or Lat ( Φ ( A ) Φ ( B ) Φ ( A ) ) = Lat ( ABA ) , or Lat ( [ Φ ( A ) , Φ ( B ) ] ) = Lat ( [ A , B ] ) .

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