Tensor product mappings. II
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- by J. R. Holub
- Proc. Amer. Math. Soc. 42 (1974), 437-441
- DOI: https://doi.org/10.1090/S0002-9939-1974-0331104-4
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Abstract:
In this paper factorization techniques are introduced into the study of tensor product mappings to complete and improve on some results obtained by the author in an earlier paper [Tensor product mappings, Math. Ann. 188 (1970), 1-12. MR 44 #2052]. The main results are as follows: Let $\alpha$ be any $\otimes$-norm. Then (i) if S is absolutely summing and T is an integral operator then $S{ \otimes _\alpha }T$ is absolutely summing, (ii) if S is quasi-nuclear and T is nuclear then $S{ \otimes _\alpha }$ T is quasi-nuclear, (iii) if S and T are integral operators then $S{ \otimes _\alpha }T$ is integral. That the results (i) and (ii) are essentially the best possible was shown by examples in the earlier quoted paper. Also, the methods developed in this paper yield a much simpler proof of the main result of the earlier paper.References
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Bibliographic Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 42 (1974), 437-441
- MSC: Primary 47B10
- DOI: https://doi.org/10.1090/S0002-9939-1974-0331104-4
- MathSciNet review: 0331104