Mathes, B., et al. “Reducible Semigroups of Idempotent Operators”. Journal of Operator Theory, vol. 40, no. 1, 1998, pp. 35-69, https://scholar2.islandarchives.ca/islandora/object/ir%3Air-batch6-1558.

Genre

  • Journal Article
Contributors
Author: Mathes, B.
Author: Radjavi, H.
Author: MacDonald, Gordon W.
Author: Livshits, L.
Date Issued
1998
Abstract

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.

Note

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
Page range
35-69
Host Title
Journal of Operator Theory
Host Abbreviated Title
J.Operat.Theor.
Volume
40
Issue
1
ISSN
0379-4024