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On the commutator of two operators in sandwiches. (Russian)
Authors: Ufnarovskij V. A.
Abstract
Let $C = AB-BA$ be a matrix of rang 1. Three different proofs, that $A$ and $B$ has nontrivial common invariant subspace are suggested. The last proof is based on the more general result: if $a$ and $b$ are generators of an associative algebra $A$ over field $K$ of zero characteristic and for $c=[a,b]$ we have $c(Ac\cap [A,A]) = 0$, then $Ac \subseteq [A,A]$.Institutul de Matematica Academia de Ştiinţe a Moldovei
str. Academiei 5, Chişinău MD-2028, Moldova
str. Academiei 5, Chişinău MD-2028, Moldova
Contents
- An algorithm for forming the Poincare cycle. (Russian)
- A property of the rings of endomorphisms. (Romanian)
- On solution of problems of integer programming. (Russian)
- Rates of queue length convergence for priority queues with orientation. (English)
- On the commutator of two operators in sandwiches. (Russian)
- Idempotents and the radical with respect to a right ideal. (Russian)
- Independence and nilpotency in algebras. (Russian)
- On isomorphisms of free topological groups, rings and modules generated by topological spaces. (Russian)
- Modeling of self-dual Boolean functions commuting with 1 in a 3-valued extension of provability-intuitionistic logic. (Russian)
- $L\sb 2$ estimates for singularly perturbed onedimensional hyperbolic equations of high order. (English)
- On the group of motions of the four-dimensional hyperbolic space of a $120$-hedron. (Russian)
