On linear operators with p-nuclear adjoints

Details On linear operators with p-nuclear adjoints On linear operators with p-nuclear adjoints

2001-07-16

arxiv.org/abs/math/0107113v1

Vestnik SPb GU, ser. Matematika, 4 (2000), 24-27 (in Russia)

Mathematics

Functional Analysis

6 pages, AMSTeX

Scientific paper

If $p\in [1,+\infty]$ and $T$ is a linear operator with $p$-nuclear adjoint from a Banach space $ X$ to a Banach space $Y$ then if one of the spaces $X^*$ or $Y^{***}$ has the approximation property, then $T$ belongs to the ideal $N^p$ of operators which can be factored through diagonal oparators $l_{p'}\to l_1.$ On the other hand, there is a Banach space $W$ such that $W^{**}$ has a basis and such that for each $p\in [1,+\infty], p\neq 2,$ there exists an operator $T: W^{**}\to W$ with $p$-nuclear adjoint that is not in the ideal $N^p,$ as an operator from $W^{**}$ to $ W.$

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