Cp |
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Authors: | Charles A McCarthy |
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Institution: | (1) University of Minnesota, 55455 Minneapolis, Minnesota |
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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.
The author was supported by National Science Foundation Grant GP-5707. |
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Keywords: | |
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