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Continuous isometric semigroups and reflexivity

Marek Ptak (1991)

Annales Polonici Mathematici

 Abstract. We consider the reflexivity of a WOT-closed algebra generated by continuous isometric semigroups parametrized by the semigroup of non-negative reals or the semigroup of finite sequences of non-negative reals. It is also proved that semigroups of continuous unilateral multi-parameter shifts are reflexive.

Contractions on probabilistic metric spaces: examples and counterexamples.

Berthold Schweizer, Howard Sherwood, Robert M. Tardiff (1988)

Stochastica

The notion of a contraction mapping for a probabilistic metric space recently introduced by T. L. Hicks is compared with the notion previously introduced by V. L. Sehgal and A. T. Bharucha-Reid. By means of appropriate examples, it is shown that these two notions are independent. It is further shown that every Hick's contraction on a PM space (S,F,tW) is an ordinary metric contraction with respect to a naturally defined metric on that space; and it is again pointed out that, in Menger spaces under...

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