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Uniqueness, strong forms of uniqueness and negative powers of contractions

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In this work we discuss several ways to extend to the context of Banach spaces the notion of Hilbert-Schmidt operator: p-summing operators, γ-summing or γ-radonifying operators, weakly* 1-nuclear operators and classes of operators defined via factorization properties. We introduce the class PS₂(E;F) of pre-Hilbert-Schmidt operators as the class of all operators u: E → F such that w ∘ u ∘ v is Hilbert-Schmidt for every bounded operator v: H₁ → E and every bounded operator w: F → H₂, where H₁ and H₂ are Hilbert spaces. Besides the trivial case where one of the spaces E or F is a ''Hilbert-Schmidt space", this space seems to have been described only in the easy situation where one of the spaces E or F is a Hilbert space.
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Boundary values of analytic semigroups and associated norm estimates

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The theory of quasimultipliers in Banach algebras is developed in order to provide a mechanism for defining the boundary values of analytic semigroups on a sector in the complex plane. Then, some methods are presented for deriving lower estimates for operators defined in terms of quasinilpotent semigroups using techniques from the theory of complex analysis.
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Discontinuous homomorphisms from C(K)

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