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General preservers of invariant subspace lattices

✍ Scribed by Gregor Dolinar; Shuanping Du; Jinchuan Hou; Peter LegiŠa

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
139 KB
Volume
429
Category
Article
ISSN
0024-3795

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✦ Synopsis

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

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