À propos d'une question posée par V. Klee
Nous répondons par la négative à une question posée par Klee (Mathematical Note no 599, Boeing Scientific Research Laboratories, p.29).
Nous répondons par la négative à une question posée par Klee (Mathematical Note no 599, Boeing Scientific Research Laboratories, p.29).
A quantitative version of Krein's Theorem on convex hulls of weak compact sets is proved. Some applications to weakly compactly generated Banach spaces are given.
We prove a uniform version of the converse Taylor theorem in infinite-dimensional spaces with an explicit relation between the moduli of continuity for mappings on a general open domain. We show that if the domain is convex and bounded, then we can extend the estimate up to the boundary.
We prove the following quasi-dichotomy involving the Banach spaces C(α,X) of all X-valued continuous functions defined on the interval [0,α] of ordinals and endowed with the supremum norm. Suppose that X and Y are arbitrary Banach spaces of finite cotype. Then at least one of the following statements is true. (1) There exists a finite ordinal n such that either C(n,X) contains a copy of Y, or C(n,Y) contains a copy of X. (2) For any infinite countable...
We present an analogue of the Harer–Zagier recursion formula for the moments of the gaussian Orthogonal Ensemble in the form of a five term recurrence equation. The proof is based on simple gaussian integration by parts and differential equations on Laplace transforms. A similar recursion formula holds for the gaussian Symplectic Ensemble. As in the complex case, the result is interpreted as a recursion formula for the number of 1-vertex maps in locally orientable surfaces with a given number of...