Abstract
We show, by presenting two examples, that a somewhat forgotten condition of Hasegawa (Proc Jpn Acad 40:262–266, 1964) is useful in proving convergence of operator semigroups, and may be more handy than the standard range condition. Also, we present the semigroup related to Blackwell’s example (Ann Math Statist 29:313–316, 1958) as an infinite product of commuting Markov semigroups. Intriguingly, it is hard to find a manageable description of the generator of this semigroup. As a result, it is much easier to prove the existence of the infinite product involved by direct argument than it is to do this using the Trotter–Kato–Sova–Kurtz–Hasegawa theory.
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Bobrowski, A. On a somewhat forgotten condition of Hasegawa and on Blackwell’s example. Arch. Math. 104, 237–246 (2015). https://doi.org/10.1007/s00013-015-0743-8
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DOI: https://doi.org/10.1007/s00013-015-0743-8