Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Tensor product mappings. II

Author: J. R. Holub
Journal: Proc. Amer. Math. Soc. 42 (1974), 437-441
MSC: Primary 47B10
MathSciNet review: 0331104
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47B10

Retrieve articles in all journals with MSC: 47B10

Additional Information

Keywords: Tensor products, absolutely summing operator, integral operator, nuclear operator, factorization of operators
Article copyright: © Copyright 1974 American Mathematical Society