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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Projections on tensor product spaces


Authors: E. J. Halton and W. A. Light
Journal: Trans. Amer. Math. Soc. 287 (1985), 161-165
MSC: Primary 41A65; Secondary 41A63, 46M05
DOI: https://doi.org/10.1090/S0002-9947-1985-0766211-7
MathSciNet review: 766211
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Abstract: $ (S,\Sigma ,\mu ),(T,\Theta ,\upsilon )$ are finite, nonatomic measure spaces. $ G$ and $ H$ are finite-dimensional subspaces of $ {L_1}(S)$ and $ {L_1}(T)$ respectively. Both $ G$ and $ H$ contain the constant functions. It is shown that the relative projection constant of $ {L_1}(S) \otimes H + G \otimes {L_1}(T)$ in $ {L_1}(S \times T)$ is at least $ 3$.


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DOI: https://doi.org/10.1090/S0002-9947-1985-0766211-7
Article copyright: © Copyright 1985 American Mathematical Society