Polynomial inequalities for non-commuting operators
نویسندگان
چکیده
منابع مشابه
Ela Polynomial Inequalities for Non-commuting Operators
We prove an inequality for polynomials applied in a symmetric way to non-commuting operators.
متن کاملOn the energy of non-commuting graphs
For given non-abelian group G, the non-commuting (NC)-graph $Gamma(G)$ is a graph with the vertex set $G$ $Z(G)$ and two distinct vertices $x, yin V(Gamma)$ are adjacent whenever $xy neq yx$. The aim of this paper is to compute the spectra of some well-known NC-graphs.
متن کاملConvergent Relaxations of Polynomial Optimization Problems with Noncommuting Variables
We consider optimization problems with polynomial inequality constraints in non-commuting variables. These non-commuting variables are viewed as bounded operators on a Hilbert space whose dimension is not fixed and the associated polynomial inequalities as semidefinite positivity constraints. Such problems arise naturally in quantum theory and quantum information science. To solve them, we intr...
متن کاملThe functional calculus for commuting row contractions
A commuting row contraction is a d-tuple of commuting operators T1, . . . , Td such that ∑d i=1 TiT ∗ i ≤ I. Such operators have a polynomial functional calculus which extends to a norm closed algebra of multipliers Ad on Drury-Arveson space. We characterize those row contractions which admit an extension of this map to a weak-∗ continuous functional calculus on the full multiplier algebra. In ...
متن کاملSelf-adjoint commuting differential operators of rank two
This is a survey of results on self-adjoint commuting ordinary differential operators of rank two. In particular, the action of automorphisms of the first Weyl algebra on the set of commuting differential operators with polynomial coefficients is discussed, as well as the problem of constructing algebro-geometric solutions of rank l > 1 of soliton equations. Bibliography: 59 titles.
متن کامل