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Given two Banach function spaces we study the pointwise product space E · F , especially for the case that the pointwise product of their unit balls is again convex. We then give conditions on when the pointwise product E ·M(E,F ) = F , where M(E,F ) denotes the space of multiplication operators from E into F .

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 is that on such a Banach space, the classes of finitely spectral and prespectral operators coincide. We also apply this result to give some sufficient conditions for an operator with an absol...

For 0 < p < 1 we give examples of Banach spaces isometrically embedding into Lp but not into any Lr with p < r ≤ 1.

The conceptual spaces approach has emerged as a new and powerful way of thinking about concepts. In earlier work, the present authors have addressed the question of how to model vague concepts in the conceptual spaces framework. That in turn was instrumental in Decock’s and Douven’s account of a graded membership relation in further work. In this paper, we make use of the account of graded memb...

Every renovation project makes use of embodied energy, increasing the energy and material footprint a building in short term. But by reusing longer-lasting layer structure, renovations can lower environmental cost architecture long term: be retrofitted with energy-efficient solutions more socially effective spaces. Felipe Alarcón's demonstrates this principle, improving performance house while...