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Unconditional ideals in Banach spaces

G. Godefroy;  N. Kalton;  P. Saphar — 1993

Studia Mathematica

We show that a Banach space with separable dual can be renormed to satisfy hereditarily an “almost” optimal uniform smoothness condition. The optimal condition occurs when the canonical decomposition X * * * = X ⊥ ⊕ X * is unconditional. Motivated by this result, we define a subspace X of a Banach space Y to be an h-ideal (resp. a u-ideal) if there is an hermitian projection P (resp. a projection P with ∥I-2P∥ = 1) on Y* with kernel X ⊥ . We undertake a general study of h-ideals and u-ideals. For example we show that...

Unsolved Problems

N. Aronszajn;  L. Gross;  S. Kwapień;  N. Nielsen;  A. Pełczyński;  A. Pietsch;  L. Schwartz;  P. Saphar;  S. Chevet;  R. Dudley;  D. Garling;  N. Kalton;  B. Mitjagin;  S. Rolewicz;  E. Schock;  J. Daleckiĭ;  J. Dobrakov;  B. Gelbaum;  G. Henkin;  L. Nachbin;  N. Peck;  L. Waelbroeck;  P. Porcelli;  M. Rao;  M. Zerner;  V. Zakharjuta — 1970

Studia Mathematica

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

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