Invariant subspaces for positive operators on locally convex solid Riesz spaces - Zafer, Ercan; Çağlar, Mert (ELSEVIER SCIENCE BV, PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS, 2007)
We prove that an x(0)-quasinilpotent semigroup S of continuous positive linear operators on a locally convex solid Riesz space X has a common invariant subspace. Using this, a result which implies the main theorem of Abramovich, Aliprantis and Burkinshaw [J. Funct. Anal. 115 (1993) 418-424] is also given.
Keywords: positive operator; semigroup; invariant subspace; quasinilpotent; weak quasinilpotent; pozitif operatör; yarıgrup; değişmeyen alt uzay; yarınilpotent; zayıf yarınilpotent