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For a compact Hausdorff space with a dense set of isolated points, we give a complete description of points of weak$^{*}$-norm continuity in the dual unit ball of the space of Banach space valued functions that are continuous when the range has the weak topology. As an application we give a complete description of points of weak-norm continuity of the unit ball of the space of vector measures when the underlying Banach space has the Radon-Nikodym property.

We study operator algebras with contractive approximate identities and their double centralizer algebras. These operator algebras can be characterized as L∞- Banach algebras with contractive approximate identities. We provide two examples, which show that given a non-unital operator algebra A with a contractive approximate identity, its double centralizer algebra M(A) may admit different operator algebra matrix norms, with which M(A) contains A as an M-ideal. On the other hand, we show that there is a unique operator algebra matrix norm on the unitalization algebra A1 of A such that A1 contains A as an M-ideal.

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Points of Weak-Norm Continuity in the Unit Ball of the Space WC(K, X)

Operator Algebras with Contractive Approximate Identities

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Points of Weak*-Norm Continuity in the Unit Ball of the Space WC(K, X)*

Operator Algebras with Contractive Approximate Identities

Points of Weak-Norm Continuity in the Unit Ball of the Space WC(K, X)