Abstract
ABSTRACT A tensor is the sum of at least elementary tensors. In addition, a ‘border rank’ is defined: holds if r is the minimum integer such that is a limit of rank-r tensors. Usually, the set of rank-r tensors is not closed, i.e. tensors with may exist. It is easy to see that in such a case the representation of rank-r tensors contains diverging elementary tensors as approaches In a first part, we recall results about the uniform strength of the divergence in the case of general nonclosed tensor formats (restricted to finite dimensions). The second part discusses the r-term format for infinite-dimensional tensor spaces. It is shown that the general situation is very similar to the behaviour of finite-dimensional model spaces. The third part contains the main result: it is proved that in the case of the divergence strength is , i.e. if and the parameters of increase at least proportionally to
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