Let C be a unital AH-algebra and let A be a unital separable simple C∗-algebra with tracial rank zero. Suppose that φ1, φ2 : C → A are two unital monomorphisms. We show that there is a continuous path of unitaries {ut : t ∈ [0,∞)} of A such that lim t→∞ u∗tφ1(a)ut = φ2(a) for all a ∈ C if and only if [φ1] = [φ2] in KK(C,A), τ ◦ φ1 = τ ◦ φ2 for all τ ∈ T (A) and the rotation map η̃φ1,φ2 associate...

Recently the author [Proc. Amer. Math. Soc. 103(1988), 11291135] proved random versions of an interesting theorem of Ky Fan [Theorem 2, Math. Z. 112 (1969), 234-240] for continuous condensing random maps and nonexpansive random maps defined on a closed convex bounded subset in a separable Hilbert space. In this paper, we prove that it is still true for (more general) continuous 1-set-contractiv...

We prove that every Banach space containing a complemented copy of c0 has an antiproximinal body for a suitable norm. If, in addition, the space is separable, there is a pair of antiproximinal norms. In particular, in a separable polyhedral space X, the set of all (equivalent) norms on X having an isomorphic antiproximinal norm is dense. In contrast, it is shown that there are no antiproximinal...

Chaotic linear dynamics deals primarily with various topological ergodic properties of semigroups of continuous linear operators acting on a topological vector space. We treat the questions of the following type. Characterize which of the spaces from a given class support a semigroup of prescribed shape satisfying a given topological ergodic property. In particular, we characterize LBS-spaces (...

We study the problem of approximating a function from a separable metric space D to a separable metric space Z by functions g from D to Z which have the property there is no set E of power 2** such that g is a homeomorphism of E onto g(E). Theorem 1 asserts that any one to one function may be approximated by such a function. Numerous continuous functions may be approximated by such functions wh...

The condition onto pair (F, G) of function Banach spaces under which there exists a integral operator T : F → G with analytic kernel such that the inverse mapping T −1 :imT → F does not belong to arbitrary a priori given Borel (or Baire) class is found. We begin with recalling some definitions [4, §31.IX]. Let X and Y be metric spaces. By definition, the family of analytically representable map...

1. In the theory of (F)-spaces,1 the following two questions arise: (A) Let £ be a metrizable locally convex space; is it true that if every bounded set in E is separable, the space E is separable? (B) Let £ be a metrizable locally convex space, E its completion; is it true that every bounded set in E is contained in the closure of a bounded set of El The purpose of this note is to prove that, ...

March 7, 2000 Abstract. A Banach space X is said to have the separable lifting property if for every subspace Y of X containing X and such that Y/X is separable there exists a bounded linear lifting from Y/X to Y . We show that if a sequence of Banach spaces E1, E2, . . . has the joint uniform approximation property and En is c-complemented in E∗∗ n for every n (with c fixed), then P n En 0 has...

We consider a Hilbert space of entire analytic functions on non-separable space, associated with Fock space. show that under some conditions operators, like the differentiation operators and translation are topologically transitive in this

We consider the problem of highly space-efficient representation of separable graphs while supporting queries in constant time in the RAM with logarithmic word size. In particular, we show constanttime support for adjacency, degree and neighborhood queries. For any monotone class of separable graphs, the storage requirement of the representation is optimal to within lower order terms. Separable...