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Let Ar = {r < |z| < 1} be an annulus. We consider the class of operators Fr := {T ∈ B(H) : rT(T) + TT ∗ ≤ r2 +… Click to show full abstract
Let Ar = {r < |z| < 1} be an annulus. We consider the class of operators Fr := {T ∈ B(H) : rT(T) + TT ∗ ≤ r2 + 1, σ(T ) ⊂ Ar} and show that for every bounded holomorphic function φ on Ar : sup T∈Fr ||φ(T )|| ≤ √ 2||φ||∞, where the constant √ 2 is the best possible. We do this by characterizing the calcular norm induced on H∞(Ar) by Fr as the multiplier norm of a suitable holomorphic function space on Ar.
Keywords:
type inequality;
neumann type;
inequality annulus;
von neumann
Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2022
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Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2022
Link to full text (if available)
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recommendations!