Centralisers of spaces of symmetric tensor products and applications |
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Authors: | Christopher Boyd Silvia Lassalle |
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Affiliation: | (1) School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland;(2) Departamento de Matemática, Pab. I – Cuidad Universitaria, (FCEN), Universidad de Buenos Aires, (1428) Buenos Aires, Argentina |
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Abstract: | We show that the centraliser of the space of n-fold symmetric injective tensors, n≥2, on a real Banach space is trivial. With a geometric condition on the set of extreme points of its dual, the space of integral polynomials we obtain the same result for complex Banach spaces. We give some applications of this results to centralisers of spaces of homogeneous polynomials and complex Banach spaces. In addition, we derive a Banach-Stone Theorem for spaces of vector-valued approximable polynomials. This project was supported in part by Enterprise Ireland, International Collaboration Grant – 2004 (IC/2004/009). The second author was also partially supported by PIP 5272,UBACYTX108 and PICT 03-15033 |
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Keywords: | Primary: 46B20 46G25 Secondary: 46B04 46B28 |
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