We give an example of a positive semigroup on a Banach lattice whose semigroup dual is not a Banach lattice.
We give an example of a positive semigroup on a Banach lattice whose semigroup dual is not a Banach lattice.
This paper, which is written within a rigorously constructive framework, deals with preference relations (strict weak orders) on a locally compact space X, and with the representation of such relations by continuous utility functions (order isomorphisms) from X into ℝ. Necessary conditions are given for finding the values of a utility function algorithmically in terms of the parameters when X is a locally compact, convex subset of RN. These conditions single out the class of admissible preference relations, which are investigated in some detail. The paper concludes with some results on the algorithmic continuity of the process which assigns utility functions to admissible preference relations.
The work of this paper can be regarded as a recursive development of preference and utility theory.
The number of full, and the number of fundamental partial orderings on a finite set are determined. Also, the structure of the partially ordered set of full suborderings of a finite chain is investigated.
A complete description is given of the eigenvalues of the matrix A associated with absolute Cesàro summability of any positive order, where A is regarded as an operator on the Banach space lp, with 1 ≤p≤ ∞.
Let p,q ∈ ℕ and let ϱ≥ϱp,q with ϱp,q = max {l/p, l/q}, ϱp1, = 1/p, and ϱ1,q= 1/q, p,q>l. In this paper it is proved that there exist symmetric differential operators Ap,q in L2(ℝ) such that the Gelfand-Shilov space Spϱpϱ is equal to the Gevrey space of order 2pqϱ relative to Ap,q.
Suppose (R, G) is a non-reduced abstract Witt ring containing a rigid element d such that the value set D<1,-d> satisfies a certain finiteness-condition. Then (R, G) is a direct product of a reduced abstract Witt ring and a Witt-group ring.
Semi-reflexivity and reflexivity of locally convex spaces over a field K with a, non-trivial, non-archimedean valuation are studied.
The key result is the following. Let A be a closed (local) compactoid in a Banach space E over a non-archimedean valued field K. If F is a K-Banach space and T:E→F is a continuous linear map then for each λ∈K, |λ|>1. As an application the existence of the finest admissible topology of countable type on a locally convex space is proved.
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