Genre
- Journal Article
We study the existence of common invariant subspaces for semigroups of idempotent operators. It is known that in finite dimensions every such semigroup is simultaneously triangularizable. The question; of the existence of even one non-trivial invariant subspace is still open in infinite dimensions. Working with semigroups of idempotent operators in Hilbert/Banach vector space settings, we exploit the connection between the purely algebraic structure and the operator structure to show that the answer is affirmative in a number of cases.
Colby Coll, Dept Math & CS, Waterville, ME 04901 USA. Univ Prince Edward Isl, Dept Math & CS, Charlottetown, PE C1A 4P3, Canada. Dalhousie Univ, Dept Math Stat & Comp Sci, Halifax, NS B3H 3J3, Canada.; Livshits, L, Colby Coll, Dept Math & CS, Wa(TRUNCATED)
BUCHAREST; C/O INST MATHEMATICS, PO BOX 1-764, BUCHAREST 70700, ROMANIA
THETA FOUNDATION
PT: J; CR: AUPETIT B, 1979, LECT NOTES MATH, V735 FILLMORE P, 1994, SEMIGROUP FORUM, V49, P195 GREEN JA, 1952, P CAMBRIDGE PHILOS S, V48, P35 KATAVOLOS A, 1990, J LOND MATH SOC, V41, P547 PETRIC M, 1977, LECT SEMIGROUPS RADJAVI H, 1973, INVARIANT SUBSPACES RADJAVI H, 1974, MATH ANN, V209, P43 RADJAVI H, 1985, J OPERAT THEOR, V13, P63; NR: 8; TC: 5; J9: J OPERAT THEOR; PG: 35; GA: 162GK
Source type: Electronic(1)
Language
- English
Subjects
- reducible
- idempotents
- semigroups
- Mathematics
- TRIANGULARIZATION
- invariant subspaces
- bands