Products of commuting nilpotent operators
نویسندگان
چکیده
Matrices that are products of two (or more) commuting square-zero matrices and matrices that are products of two commuting nilpotent matrices are characterized. Also given are characterizations of operators on an infinite dimensional Hilbert space that are products of two (or more) commuting square-zero operators, as well as operators on an infinite-dimensional vector space that are products of two commuting nilpotent operators.
منابع مشابه
The Sums and Products of Commuting AC-Operators
Abstract: In this paper, we exhibit new conditions for the sum of two commuting AC-operators to be again an AC-operator. In particular, this is satisfied on Hilbert space when one of them is a scalar-type spectral operator.
متن کاملNew BRST Charges in RNS Superstring Theory and Deformed Pure Spinors
We show that new BRST charges in RNS superstring theory with nonstandard ghost numbers, constructed in our recent work, can be mapped to deformed pure spinor (PS) superstring theories, with the nilpotent pure spinor BRST charge QPS = ∮ λdα still retaining its form but with singular operator products between commuting spinor variables λ. Despite the OPE singularities, the pure spinor condition λ...
متن کاملPseudo-riemannian Manifolds with Commuting Jacobi Operators
We study the geometry of pseudo-Riemannian manifolds which are Jacobi–Tsankov, i.e. J (x)J (y) = J (y)J (x) for all x, y. We also study manifolds which are 2-step Jacobi nilpotent, i.e. J (x)J (y) = 0 for all x, y.
متن کاملThe upper bound for the index of nilpotency for a matrix commuting with a given nilpotent matrix
We consider the following problem: What are possible sizes of Jordan blocks for a pair of commuting nilpotent matrices? Or equivalently, for which pairs of nilpotent orbits of matrices (under similarity) there exists a pair of matrices, one from each orbit, that commute. The answer to the question could be considered as a generalization of Gerstenhaber– Hesselink theorem on the partial order of...
متن کاملA 3× 3 Dilation Counterexample
We define four 3×3 commuting contractions which do not dilate to commuting isometries. However they do satisfy the scalar von Neumann inequality. These matrices are all nilpotent of order 2. We also show that any three 3×3 commuting contractions which are scalar plus nilpotent of order 2 do dilate to commuting isometries.
متن کامل