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Invariant subspaces and spectral conditions on operator semigroups. (English) Zbl 0931.47006

Janas, Jan (ed.) et al., Linear operators. Proceedings of the semester organized at the Stefan Banach International Mathematical Center, Warsaw, Poland, February 7–May 15, 1994. Warsaw: Polish Academy of Sciences, Inst. of Mathematics, Banach Cent. Publ. 38, 287-296 (1997).
This is a brief, however a well written survey on the problem of existence of common invariant nontrivial subspaces for semigroups of operators acting in finite or infinite-dimensional Hilbert spaces. Some proofs are outlined and unanswered questions are formulated.
For the entire collection see [Zbl 0863.00036].

MSC:

47A15 Invariant subspaces of linear operators
47D03 Groups and semigroups of linear operators
20M20 Semigroups of transformations, relations, partitions, etc.
15A30 Algebraic systems of matrices
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