Twisted sums with $C(K)$ spaces

Twisted Sums with C(k) Spaces

If X is a separable Banach space, we consider the existence of non-trivial twisted sums 0 → C(K) → Y → X → 0, where K = [0, 1] or ωω . For the case K = [0, 1] we show that there exists a twisted sum whose quotient map is strictly singular if and only if X contains no copy of `1. If K = ωω we prove an analogue of a theorem of Johnson and Zippin (for K = [0, 1]) by showing that all such twisted s...

Twisted Sums , Fenchel - Orlicz Spaces

A twisted sum Z of two Banach spaces X and Y is defined (see [11]) through a short exact sequence: 0 −→ X −→ Z −→ Y −→ 0. These short exact sequences in the category of (quasi-)Banach spaces are considered naturally in the investigation of three space properties (a property P in the category of quasi-Banach spaces is called a three space property if for every short exact sequence as above, Z ha...

Twisted T -adic Exponential Sums

The L-function and C-function of twisted T -adic exponential sums are defined. The Hodge bound for the T -adic Newton polygon of the C-function is established. As an application, the T -adic Newton polygons of the L-functions of twisted p-power order exponential sums associated to diagonal forms are explicitly given. 1. Preliminaries Let Fq be the field of characteristic p with q elements, and ...

Complex Interpolation and Twisted Twisted Hilbert Spaces

Newton Polygons for Twisted Exponential Sums

We study the p-adic absolute value of the roots of the L-functions associated to certain twisted character sums, and additive character sums associated to polynomials P (x d), when P varies among the space of polynomial of fixed degree e over a finite field of characteristic p. For sufficiently large p, we determine in both cases generic Newton polygons for these L-functions, which is a lower b...