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Suppose that $(\Omega ,\mathcal{M},\mu )$ is a $\sigma $-finite measure space, $1

In this note, we show that if a Banach space X has a predual, then every bounded linear operator on X with a continuous functional calculus admits a bounded Borel functional calculus. A consequence of this result is that on such a Banach space, the classes of finitely spectral and prespectral operators coincide. We also apply our theorem to give some sufficient conditions for an operator with an absolutely continuous functional calculus to admit a bounded Borel one. [ABSTRACT FROM AUTHOR]

Let X be a closed linear subspace of the Lebesgue space Lp(Ω; μ) for some 1 < p < ∞, and let − A be an invertible operator that is the generator of a bounded holomorphic semigroup Tt on X. Then for each 0 < α < 1 the maximal function supt>0 |Ttf(x)| belongs to Lp(Ω; μ) for each f in the domain of Aα. If moreover iA generates a bounded C0-group and A has spectrum contained in (0, ∞), then A has a bounded H∞ functional calculus. [ABSTRACT FROM PUBLISHER]

In this paper, we will extend the bilinear multiplier symbols of operators to bilinear operators on ℝ using transference techniques. [ABSTRACT FROM AUTHOR]