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TBDmathscidoc:1701.333124

Arkiv for Matematik, 46, (1), 7-29, 2006.9
Decomposable mappings from the space of symmetric\$k\$-fold tensors over\$E\$, \$\bigotimes_{s,k}E\$ , to the space of\$k\$-fold tensors over\$F\$, \$\bigotimes_{s,k}F\$ , are those linear operators which map nonzero decomposable elements to nonzero decomposable elements. We prove that any decomposable mapping is induced by an injective linear operator between the spaces on which the tensors are defined. Moreover, if the decomposable mapping belongs to a given operator ideal, then so does its inducing operator. This result allows us to classify injective linear operators between spaces of homogeneous approximable polynomials and between spaces of nuclear polynomials which map rank-1 polynomials to rank-1 polynomials.
```@inproceedings{christopher2006decomposable,
title={Decomposable symmetric mappings between infinite-dimensional spaces},
author={Christopher Boyd, and Silvia Lassalle},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203621991508933},
booktitle={Arkiv for Matematik},
volume={46},
number={1},
pages={7-29},
year={2006},
}
```
Christopher Boyd, and Silvia Lassalle. Decomposable symmetric mappings between infinite-dimensional spaces. 2006. Vol. 46. In Arkiv for Matematik. pp.7-29. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203621991508933.