We construct a semigroup of bounded idempotents with no nontrivial invariant closed subspace. This answers a question which was open for some time.
@article{bwmeta1.element.bwnjournal-article-smv125i1p97bwm, author = {Roman Drnov\v sek}, title = {An irreducible semigroup of idempotents}, journal = {Studia Mathematica}, volume = {122}, year = {1997}, pages = {97-99}, zbl = {0886.47005}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv125i1p97bwm} }
Drnovšek, Roman. An irreducible semigroup of idempotents. Studia Mathematica, Tome 122 (1997) pp. 97-99. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv125i1p97bwm/
[00000] [1] P. Fillmore, G. MacDonald, M. Radjabalipour and H. Radjavi, Towards a classification of maximal unicellular bands, Semigroup Forum 49 (1994), 195-215. | Zbl 0811.20061
[00001] [2] D. Hadwin, E. Nordgren, M. Radjabalipour, H. Radjavi and P. Rosenthal, A nil algebra of bounded operators on Hilbert space with semisimple norm closure, Integral Equations Operator Theory 9 (1986), 739-743. | Zbl 0631.47034
[00002] [3] H. Radjavi, On the reduction and triangularization of semigroups of operators, J. Operator Theory 13 (1985), 65-71. | Zbl 0581.47026
[00003] [4] H. Radjavi, Invariant subspaces and spectral conditions on operator semigroups, in: Linear Operators, Banach Center Publ. 38, Inst. Math., Polish Acad. Sci., 1997, 287-296. | Zbl 0931.47006