scholarly journals General preservers of invariant subspace lattices

2008 ◽  
Vol 429 (1) ◽  
pp. 100-109 ◽  
Author(s):  
Gregor Dolinar ◽  
Shuanping Du ◽  
Jinchuan Hou ◽  
Peter LegiŠa
Keyword(s):  
Invariant Subspace ◽  
Subspace Lattices

Examples of invariant subspace lattices

1970 ◽  
Vol 37 (1) ◽  
pp. 103-112 ◽  
Author(s):  
Peter Rosenthal
Keyword(s):  
Invariant Subspace ◽  
Subspace Lattices

Examples of Invariant Subspace Lattices

1973 ◽  
pp. 60-83
Author(s):  
Heydar Radjavi ◽  
Peter Rosenthal
Keyword(s):  
Invariant Subspace ◽  
Subspace Lattices

Remarks on Invariant Subspace Lattices

1969 ◽  
Vol 12 (5) ◽  
pp. 639-643 ◽  
Author(s):  
Peter Rosenthal
Keyword(s):  
Hilbert Space ◽  
Linear Operator ◽  
Invariant Subspace ◽  
Complete Lattice ◽  
Bounded Linear Operator ◽  
Complex Hilbert Space ◽  
Subspace Lattice ◽  
Bounded Linear ◽  
Infinite Dimensional ◽  
Subspace Lattices

If A is a bounded linear operator on an infinite-dimensional complex Hilbert space H, let lat A denote the collection of all subspaces of H that are invariant under A; i.e., all closed linear subspaces M such that x ∈ M implies (Ax) ∈ M. There is very little known about the question: which families F of subspaces are invariant subspace lattices in the sense that they satisfy F = lat A for some A? (See [5] for a summary of most of what is known in answer to this question.) Clearly, if F is an invariant subspace lattice, then {0} ∈ F, H ∈ F and F is closed under arbitrary intersections and spans. Thus, every invariant subspace lattice is a complete lattice.

scholarly journals Invariant subspace lattices that complement every subspace

1988 ◽  
Vol 32 (1) ◽  
pp. 151-158
Author(s):  
Che-Kao Fong ◽  
Domingo A. Herrero ◽  
Leiba Rodman
Keyword(s):  
Invariant Subspace ◽  
Subspace Lattices
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