We present a model of truthful elicitation which generalizes and extends mechanisms, scoring rules, and a number of related settings that do not quite qualify as one or the other. Our main result is a characterization theorem, yielding characterizations for all of these settings, including a new characterization of scoring rules for non-convex sets of distributions. We generalize this model to ...

For a Boolean function f, let D(f) denote its deterministic decision tree complexity, i.e., minimum number of (adaptive) queries required in worst case in order to determine f. In a classic paper, Rivest and Vuillemin [19] show that any non-constant monotone property P : {0, 1}( n 2) → {0, 1} of n-vertex graphs has D(P) = Ω(n). We extend their result to 3-uniform hypergraphs. In particular, we ...

The James–Schreier spaces Vp, where 1 6 p < ∞, were recently introduced by Bird and Laustsen [5] as an amalgamation of James’ quasi-reflexive Banach space on the one hand and Schreier’s Banach space giving a counterexample to the Banach–Saks property on the other. The purpose of this note is to answer some questions left open in [5]. Specifically, we prove that (i) the standard Schauder basis f...

X iv :m at h/ 94 03 21 2v 1 [ m at h. FA ] 3 1 M ar 1 99 4 CLASSES OF BANACH SPACES STABLE AND UNSTABLE WITH RESPECT TO THE OPENING M.I.Ostrovskii Mathematics Department, Boǧaziçi University 80815 Bebek, Istanbul, TURKEY and Mathematical Division, Institute for Low Temperature Physics 47 Lenin avenue, 310164 Kharkov, UKRAINE e-mail: [email protected] Abstract. The paper is a complement...

We have introduced a new sequence space l(r,s,t, p;Δ(m) ) combining by using generalized means and difference operator of order m . Some topological properties as well as geometric properties namely Banach-Saks property of type p and uniform Opial property have been studied. Furthermore, the α -, β -, γ duals of this space are computed and also obtained necessary and sufficient conditions for s...

In this note, we will discuss how to relate an operator ideal on Banach spaces to the sequential structures it defines. Concrete examples of ideals of compact, weakly compact, completely continuous, Banach-Saks and weakly Banach-Saks operators will be demonstrated.