Positive linear functionals and the order cone
نویسندگان
چکیده
منابع مشابه
The Gelfand transform, positive linear functionals, and positive-definite functions
In this note, unless we say otherwise every vector space or algebra we speak about is over C. If A is a Banach algebra and e ∈ A satisfies xe = x and ex = x for all x ∈ A, and also ‖e‖ = 1, we say that e is unity and that A is unital. If A is a unital Banach algebra and x ∈ A, the spectrum of x is the set σ(x) of those λ ∈ C for which λe−x is not invertible. It is a fact that if A is a unital B...
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For k even, let Pk denote the vector space of polynomials in 2 real variables of degree at most k. A linear functional L : Pk −→ R is positive if p ∈ Pk, p|R2 ≥ 0 =⇒ L(p) ≥ 0. Hilbert’s theorem on sums of squares (cf. [15]) implies that L : P4 −→ R is positive if and only if the moment matrix associated to L is positive semidefinite. In this note, using k = 6, we exhibit the first families of p...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1989
ISSN: 0024-3795
DOI: 10.1016/0024-3795(89)90573-9