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H ∞ functional calculus for sectorial and bisectorial operators

Giovanni Dore, Alberto Venni (2005)

Studia Mathematica

We give a concise exposition of the basic theory of H ∞ functional calculus for N-tuples of sectorial or bisectorial operators, with respect to operator-valued functions; moreover we restate and prove in our setting a result of N. Kalton and L. Weis about the boundedness of the operator f ( T ₁ , . . . , T N ) when f is an R-bounded operator-valued holomorphic function.

Homomorphisms on algebras of Lipschitz functions

Fernanda Botelho, James Jamison (2010)

Studia Mathematica

We characterize a class of *-homomorphisms on Lip⁎(X,𝓑(𝓗 )), a non-commutative Banach *-algebra of Lipschitz functions on a compact metric space and with values in 𝓑(𝓗 ). We show that the zero map is the only multiplicative *-preserving linear functional on Lip⁎(X,𝓑(𝓗 )). We also establish the algebraic reflexivity property of a class of *-isomorphisms on Lip⁎(X,𝓑(𝓗 )).

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