Abstract
The spacec p is the class of operators on a Hilbert space for which thec p norm |T| p =[trace(T*T)p/2]1/p is finite. We prove many of the known results concerningc p in an elementary fashion, together with the result (new for 1<p<2) thatc p is as uniformly convex a Banach space asl p. In spite of the remarkable parallel of norm inequalities in the spacesc p andl p, we show thatp ≠ 2, noc p built on an infinite dimensional Hilbert space is equivalent to any subspace of anyl p orL p space.
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The author was supported by National Science Foundation Grant GP-5707.
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McCarthy, C.A. Cp . Israel J. Math. 5, 249–271 (1967). https://doi.org/10.1007/BF02771613
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DOI: https://doi.org/10.1007/BF02771613