On the dual of a certain operator ideal

Racher, Gerhard

doi:10.1090/S0002-9939-1981-0603597-X

On the dual of a certain operator ideal
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by Gerhard Racher

Proc. Amer. Math. Soc. 82 (1981), 36-38

DOI: https://doi.org/10.1090/S0002-9939-1981-0603597-X

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Abstract:

For complex Banach spaces $E$ and $F$ and a real number $1 < p < \infty$ let ${S^p}(E,F)$ denote the operator ideal obtained by complex interpolation between the nuclear and the compact operators. If $E$ and $F$ are reflexive and one of them has the approximation property the dual of ${S^p}(E,F)$ is shown to be ${S^{p’}}(E’,F’)$, $p’$ conjugate to $p$.

References

A.-P. Calderón, Intermediate spaces and interpolation, the complex method, Studia Math. 24 (1964), 113–190. MR 167830, DOI 10.4064/sm-24-2-113-190
Michael Cwikel, Complex interpolation spaces, a discrete definition and reiteration, Indiana Univ. Math. J. 27 (1978), no. 6, 1005–1009. MR 511254, DOI 10.1512/iumj.1978.27.27068
A. Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Séminaire Bourbaki, Vol. 2, Soc. Math. France, Paris, 1995, pp. Exp. No. 69, 193–200 (French). MR 1609222
Albrecht Pietsch and Hans Triebel, Interpolationstheorie für Banachideale von beschränkten linearen Operatoren, Studia Math. 31 (1968), 95–109 (German). MR 243341, DOI 10.4064/sm-31-1-95-109

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