Tensor products and Banach ideals of p-compact operators |
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| Authors: | Jan H Fourie Johan Swart |
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| Institution: | (1) Department of Mathematics, Potchefstroom University, 2520 Potchefstroom, South Africa;(2) Department of Mathematics, Rand Afrikaans University, P.O. Box 524, 2000 Johannesburg, South Africa;(3) National Research Institute for Mathematical Sciences of the CSIR, P.O. Box 395, 0001 Pretoria, South Africa |
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| Abstract: | A study is made of the norm wp (1  p  ) on the tensor product of two Banach spaces E and F. It is shown that wp is a tensor norm, and a representation is deduced for the elements in the completion
of E  F equipped with wp. Finally it is shown that the wp-nuclear operators in the sense of Grothendieck 3] coincide with those operators factoring compactly throughp (if 1 p ) or Co (if p=), with related equalities concerning the idea1 norms. |
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