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Revised June 25, 2010: I will share here my own very partial observations on feel I need to close this questioncircle. In this file I explain in detail Thanks for the problem, and answers given but they have all been quite off the answer in some specific examplesmark. My partial results on this problem (there is much room for improvement) as well as an application to operator theory can be found in this link: http://arxiv.org/abs/1003.0502

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I will share here my own very partial observations on this question. In this file I explain in detail the problem, and the answer in some specific examples.