Instytut Matematyczny Polskiej Akademii Nauk / pl / Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

Streszczenie

We provide conditions on a dual Banach space $X^*$ with a subsymmetric weak$^*$ Schauder basis which allow us to ensure that for any bounded operator $T \colon X^*\to X^*$, either $T(X^*)$ or $({\rm Id}_{X^*}-T)(X^*)$ contains a subspace that is isomorphic to $X^*$ and complemented in $X^*$. Under the same conditions on $X^*$, we prove that $\ell ^p(X^*)$, $1\leq p \leq \infty$, is primary. Moreover, we show that these conditions are satisfied by a wide range of Orlicz and Lorentz sequence spaces.