An irreducible semigroup of idempotents

Roman Drnovšek

Studia Mathematica (1997)

  • Volume: 125, Issue: 1, page 97-99
  • ISSN: 0039-3223

Abstract

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We construct a semigroup of bounded idempotents with no nontrivial invariant closed subspace. This answers a question which was open for some time.

How to cite

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Drnovšek, Roman. "An irreducible semigroup of idempotents." Studia Mathematica 125.1 (1997): 97-99. <http://eudml.org/doc/216425>.

@article{Drnovšek1997,
abstract = {We construct a semigroup of bounded idempotents with no nontrivial invariant closed subspace. This answers a question which was open for some time.},
author = {Drnovšek, Roman},
journal = {Studia Mathematica},
keywords = {invariant subspaces; idempotents; operator semigroups; semigroup of bounded idempotents; invariant closed subspace},
language = {eng},
number = {1},
pages = {97-99},
title = {An irreducible semigroup of idempotents},
url = {http://eudml.org/doc/216425},
volume = {125},
year = {1997},
}

TY - JOUR
AU - Drnovšek, Roman
TI - An irreducible semigroup of idempotents
JO - Studia Mathematica
PY - 1997
VL - 125
IS - 1
SP - 97
EP - 99
AB - We construct a semigroup of bounded idempotents with no nontrivial invariant closed subspace. This answers a question which was open for some time.
LA - eng
KW - invariant subspaces; idempotents; operator semigroups; semigroup of bounded idempotents; invariant closed subspace
UR - http://eudml.org/doc/216425
ER -

References

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  1. [1] P. Fillmore, G. MacDonald, M. Radjabalipour and H. Radjavi, Towards a classification of maximal unicellular bands, Semigroup Forum 49 (1994), 195-215. Zbl0811.20061
  2. [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. Zbl0631.47034
  3. [3] H. Radjavi, On the reduction and triangularization of semigroups of operators, J. Operator Theory 13 (1985), 65-71. Zbl0581.47026
  4. [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. Zbl0931.47006

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