Operators With the Single Valued Extension Property

Inherited Properties Through the Helton Class of an Operator

“…We combine the equations (12) and (13) to obtain A n = A n+1 for every nonnegative integer n, and from (12) we get that A n = 1 for every nonnegative integer n. This implies β n = α n for every nonnegative integer n. Thus we have W = R. □ …”

“…(1) Assume that at least one of the equalities σ(R) = σ e (R) = σ le (R) fails to hold or σ le (R) ̸ = σ re (R). Since σ R (x) ⊂ σ S (x) for all x ∈ H by Corollary 3.4.5 in [14] and R has the single valued extension property, it follows from [12] and [14] that S has the single valued extension property,…”

“…If S * has the single valued extension property, then from [12] we can get that R * has the single valued extension property. Thus σ(S…”

Some Remarks on the Helton Class of an Operator

“…If S ∈ Helton k (R) and R has the single valued extension property, then S has the single valued extension property from [7]. Next, let f (λ) be an analytic function which verifies (λ − S)f (λ) = x.…”

“…(4) By [7], S has the single valued extension property. Assume that x and y are any vectors in H such that σ S (x) ∩ σ S (y) = ∅.…”