Abstract
In this chapter we study the spaces of bilinear forms and operators that can be generated from a tensor norm. For each tensor norm α, we have the α-integral and the α-nuclear forms or operators. We introduce the concept of a Banach operator ideal and we develop just enough of the theory to explain the relationship between tensor norms and operator ideals. In particular, we see that the α-integral and α-nuclear classes constitute the maximal and minimal ideals respectively.
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© 2002 Springer-Verlag London
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Ryan, R.A. (2002). Operator Ideals. In: Introduction to Tensor Products of Banach Spaces. Springer Monographs in Mathematics. Springer, London. https://doi.org/10.1007/978-1-4471-3903-4_8
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DOI: https://doi.org/10.1007/978-1-4471-3903-4_8
Publisher Name: Springer, London
Print ISBN: 978-1-84996-872-0
Online ISBN: 978-1-4471-3903-4
eBook Packages: Springer Book Archive