Reducibility of semigroups and nilpotent commutators with idempotents of rank two

Matjaž Omladič, Heydar Radjavi

Abstract


Let f be a noncommutative polynomial in two variables. Let S be a multiplicative semigroup of linear operators on a finite-dimensional vector space and T a fixed linear operator such that f(T, S) is nilpotent for all S in S. In [H. Radjavi, M. Omladič, Nilpotent commutators and reducibility of semigroups, Lin. and Multilin. Alg. 57 (2009), 307-317] the authors proposed questions, what one can say about the invariant subspace structure of S under this and other related conditions. In particular, they study the question under the condition that [S, T]2 = 0, where T is a given idempotent of rank one. In this paper we extend some of the results given there to the case that T is a given idempotent of rank two.

Keywords


Reducibility, semigroups, commutators, nilpotent operators.

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DOI: https://doi.org/10.26493/1855-3974.146.279

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications