ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

1. Logic

1991 MS Classification: 46S30, 03F60 Dediu, Luminitza Simona, University of Waikato, New Zealand A constructive extension theorem for ultraweakly continuous linear functionals Let R be a linear subset of B(H) whose unit ball is totally bounded in the weak–operator topology (the weakest topology with respect to which the mappings T ↦ ⟨T x, y⟩ are continuous on B(H) for all x, y in H), and let f be a linear functional on R that is ultraweakly continuous—that is, uniformly continuous on R_{1} with respect to the weak–operator topology. We prove, within Bishop’s constructive mathematics, that f has the form T ↦ ∑_{n=1}^{∞} ⟨T x_{n}, y_{n}⟩ , where the series ∑_{n=1}^{∞} ∥x_{n}∥^{2} and ∑_{n=1}^{∞} ∥y_{n}∥^{2} converge in R. Not only does this provide an extension theorem for ultraweakly continuous linear functionals, but also, in the case R = B(H), it gives a new constructive proof of the characterisation of such functionals on B(H).