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Some Ramsey type theorems for normed and quasinormed spaces

C. HensonNigel KaltonN. PeckIgnác TereščákPavol Zlatoš — 1997

Studia Mathematica

We prove that every bounded, uniformly separated sequence in a normed space contains a “uniformly independent” subsequence (see definition); the constants involved do not depend on the sequence or the space. The finite version of this result is true for all quasinormed spaces. We give a counterexample to the infinite version in L p [ 0 , 1 ] for each 0 < p < 1. Some consequences for nonstandard topological vector spaces are derived.

Unsolved Problems

1. The operator ideals and measures in linear spaces 469-472 2. Schauder bases and linear topological invariants 473-478 3. Various problems 479-483

Short Summaries

S. CHEVET, p-ellipsoïdes de l 2 . Mesures cylindriques gaussiennes 439-441 W. WOJTYŃSKI On conditional bases in non-nuclear Fréchet spaces 441 C. BESSAGA, A theorem on complemented subspaces of nuclear spaces 441-442 C. MCCARTHY, Optimal conditioning of operators 442-443 D. PRZEWORSKA-ROLEWICZ, On algebraic derivative 443-444 N. TOMCZAK, A remark (p,q)-absolutely summing operators in L p -spaces 444-445 W. MLAK, Decompositions of operator representations of function algebras 445-446 A. PERSSON, p-integral...

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