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The existence of viable solutions of set-valued Ito equation, i.e. solutions remaining at any time in a fixed subset of a state space, is established for inclusion with dissipative set valued operators.
We investigate the topology of the spaces of order-preserving functionales O(X) over compacta X. It is shown that the space O(X) is homeomorphic to the Tychonov cube [I^tau] iff X is openly generated chi-homogeneous compactum of weight tau.
We give some conditions under which commuting triangular maps have a common fixed point. Some of them provide analogons of known results for maps of a real interval.
In this paper we examine families of common summands and anti-summands of compact convex sets. In particular, we prove the equivalence of minimality problems for common anti-summands and minimal pairs of compact convex sets. We also give partial answers to the question whether minimal anti-summands of polytopes are polytopes as well.
In this paper we present some results about weakly compact homomorphisms from a uniform algebra A into a uniform Algebra B, which is an integral domain. The main result says that if h : A -> B is a weakly compact homomorphism then h*(Sigma[B]) meets one, and only one, Gleason part of the spectrum Sigma[A] of A.
In this paper we study the duality for locally convex modules over the unit disk of a spherically complete valued field. We consider a dual pair for arbitrary locally convex B[K]-modules and pairs consisting of a locally convex module and its dual. We prove that the Mackey topology for an arbitrary locally convex B[K]-module exists. This extends some results of Van Tiel [1] obtained for locally convex...
Let alpha be a nondenumerable regular ordinal, fi any ordinal, X a Banach space. We introduce a closed subspace X[...] of the X[s] defined in [7] and of the X[alfa] defined in [6] to get a way to generate new Banach spaces non-isomorphic to their cartesian squares. In particular we obtain new Banach spaces X and Y non-isomorphic to their cartesian squares but having the property that X [...] Y is...
It is shown that in the space of all nonexpansive continuous IFS's defined on a compact convex subset of R^n the family of asymptotically stable IFS's having a singular stationary distribution is generic.
If E is a real separable Frechet space, we prove that every non void domain Omega of E is open for a continuous semi-norm is a domain of analytic existence. In particular, every non void, open and convex subset Omega of E is a domain of analytic existence. Moreover, this result cannot be improved in the case of an arbitrary real separable Frechet space. In fact, in the space omega of real sequences,...
The spaces of Borel probabilities on a topological space X inherit a number of topological properties of X. We show in particular that the space of tight probabilities on a Cech-analytic space is Cech-analytic. Analogical results are shown for several other classes of generalized analytic and complete topological spaces.
We prove certain vector-valued continuous inclusions for Calderon-Lozanovskij spaces and, by interpolation, we obtain results on the type and cotype of these spaces. We also give an extension of Kwapień's result which states that, for [1 is less than or equal to p is less than or equal to 2], every operator from l[sub 1] into l[sub p] is (r,1)-summing, if 1/r=3/2 - 1/p.
We introduce and establish some basic properties of the tame rational functions. The class of these functions contains all the rational functions with no recurrent critical points in their Julia sets. For tame non-exceptional functions we prove that the Lipschitz conjugacy, the same spectra of moduli of derivatives at periodic orbits and conformal conjugavcy are mutually equivalent. We prove also...
We try to characterize q.m.p. using quasi-eigenfunctions and generating Markov partitions. As a result we get some examples of processes which are not q.m.p. and an example of a process satisfying some weaker conditions, than the quasi-Markovian one.
Refining two Marciszewski's constructions, we present an example of a line-free group with no continuous functions onto its own square, and we give a new proof showing that van Mill's space L [6] is not homeomorphic to L x Z for any nontrival Z.
In the paper we prove a strong comparison theorem for multidimensional Ito processes with respect to a local martingale. In the particular case of a Wiener process, a more general result is proved.
It is shown that for any Hausdorff compactum X in the hyperspace C(X) of subcontinua of X (in the hyperspace 2^X of all nonempty closed subsets of X) local connectedness and local arcwise connectedness are equivalent at any point. If X has the property of Kelley, then local connectedness of C(X) is proved to be equivalent to some stronger kinds of local connectedness and of local arcwise connectedness.
In the paper, a variance-optimal hedging of a contingent claim for a discrete time model with transaction costs is considered. Existence of an optimal hedging strategy is shown.
Let X be a Banach space, C a closed subset of X, and T : C --> C a nonexpansive mapping. Conditions are given which assure that if the fixed point set F(T) of T has nonempty interior then the Picard iterates of the mapping T always converge to a point of F(T). If T is asymptotically regular, it suffices to assume that the closed subsets of X are densely proximinal and that nested spheres in X have...
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