- Cite this article as:
- McCarthy, C.A. Israel J. Math. (1967) 5: 249. doi:10.1007/BF02771613
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The spacecp is the class of operators on a Hilbert space for which thecp norm |T|p=[trace(T*T)p/2]1/p is finite. We prove many of the known results concerningcp in an elementary fashion, together with the result (new for 1<p<2) thatcp is as uniformly convex a Banach space aslp. In spite of the remarkable parallel of norm inequalities in the spacescp andlp, we show thatp ≠ 2, nocp built on an infinite dimensional Hilbert space is equivalent to any subspace of anylp orLp space.