Israel Journal of Mathematics

, Volume 5, Issue 4, pp 249–271

Cp

  • Charles A. McCarthy
Article

DOI: 10.1007/BF02771613

Cite this article as:
McCarthy, C.A. Israel J. Math. (1967) 5: 249. doi:10.1007/BF02771613

Abstract

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.

Copyright information

© Hebrew University 1967

Authors and Affiliations

  • Charles A. McCarthy
    • 1
  1. 1.University of MinnesotaMinneapolis