On general denting points and the unique positive extension of certain positive linear functionals

on the effect of linear & non-linear texts on students comprehension and recalling

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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...

An Inequality for Linear Positive Functionals

Using P0-simple functionals, we generalise the result from Theorem 1.1 obtained by Professor F. Qi (F. QI, An algebraic inequality, RGMIA Res. Rep. Coll., 2(1) (1999), article 8).

Positive linear functionals without representing measures

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...

Linear Functionals on Certain Banach Spaces