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arXiv · 2010.01573

On the complete metrisability of spaces of contractive semigroups

Raj Dahya
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Abstract

The space of unitary $C_{0}$-semigroups on separable infinite dimensional Hilbert space, when viewed under the topology of uniform weak convergence on compact subsets of $\mathbb{R}_{+}$, is known to admit various interesting residual subspaces. Before treating the contractive case, the problem of the complete metrisability of this space was raised in [Eisner, 2010]. Utilising Borel complexity computations and automatic continuity results for semigroups, we obtain a general result, which in particular implies that the one-/multiparameter contractive $C_{0}$-semigroups constitute Polish spaces and thus positively addresses the open problem.

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BibTeXRIS

Raj Dahya. 2020-10-04. On the complete metrisability of spaces of contractive semigroups. https://doi.org/10.1007/s00013-022-01717-1

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