Continuous extensions of multifunctions
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.
We prove three theorems on linear operators induced by rearrangement of a subsequence of a Haar system. We find a sufficient and necessary condition for to be continuous for 0 < p < ∞.
On montre que si est une contraction à spectre dénombrable et telle que, pour tout
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...