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Invariant Subspace Theorems for Positive Operators

✍ Scribed by Y.A. Abramovich; C.D. Aliprantis; O. Burkinshaw

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
665 KB
Volume
124
Category
Article
ISSN
0022-1236

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✦ Synopsis

We establish new invariant subspace theorems for positive operators on Banach lattices. Here are three sample results.

  • If a quasinilpotent positive operator (S) dominates a non-zero compact operator (K) (i.e., (|K x| \leqslant S|x|) for each (x) ), then every positive operator that commutes with (S), in particular (S) itself, has a non-trivial closed invariant ideal.
  • If a positive kernel operator commutes with a quasinilpotent positive operator, then both operators have a common non-trivial closed invariant subspace.
  • Every quasinilpotent positive Dunford-Pettis operator has a non-trivial closed invariant subspace. 1994 Academic Press, Inc

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