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In this article we study a natural weakening – which we refer to as paratransitivity – of the well-known notion of transitivity of an algebra AA of linear operators acting on a finite-dimensional vector space VV. Given positive integers k and m, we shall say that such an algebra AA is (k,m)(k,m)...
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In this paper, the authors continue the analysis, first undertaken in Livshits et al. (2013) [2], of algebras AA of linear transformations on an n-dimensional complex vector space VV which have the property that if WW is a k-dimensional subspace of VV, then the image of WW under the action of the al...
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Any pure operator band can be expanded so that each component of the band is reflexive.
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A multiplicative semigroup of idempotent operators is called an operator band. We prove that for each K > 1 there exists an irreducible operator band on the Hilbert space l(2) which is norm-bounded by K. This implies that there exists an irreducible operator band on a Banach space such that each ...
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We focus on matrix semigroups (and algebras) on which rank is commutable [rank(AB) = rank(BA)]. It is shown that in a number of cases (for example, in dimensions less than 6), but not always, commutativity of rank entails permutability of rank [rank(A(1)A(2)...A(n)) = rank(A(sigma(1))A(sigma(2))... ...
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