Abstract
Let m ⩽ n and C m× be the set of all m × n complex matrices. Suppose l ⩽ k ⩽ m and p ⩾ 1. For A ∈ C m× with singular values a 1 ⩾ … ⩾ am , define the (p,k) norm of A as Many authors have studied the linear operators on that preserve the (p k) norms and their structures have been determined except for cases p > 1 and 1 < k < m < n. In this note we extend the known results to these remaining cases. Further generalization of the result is also discussed.
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