An Operator Extension of Bohr’s Inequality
نویسندگان
چکیده
T φ(At)dμ(t) for every linear functional φ in the norm dual A of A; cf. [3, Section 4.1]. Further, a field (φt)t∈T of positive linear mappings φ : A → B between C -algebras of operators is called continuous if the function t 7→ φt(A) is continuous for every A ∈ A. If the C-algebras include the identity operators, denoted by the same I, and the field t 7→ φt(I) is integrable with integral I, we say that (φt)t∈T is unital. The classical Bohr’s inequality states that for any z, w ∈ C and any positive real numbers r, s with 1 r + 1 s = 1, |z + w| ≤ r|z| + s|w|.
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