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Tensor products of almost $r$-summing maps

Universitat de Barcelona
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If $T_1$ and $T_2$ are continuous linear maps on locally convex spaces, we prove that $T_1\otimes T_2$ is almost $r$-summing if and only $T_1$ and $T_2$ so are. We also obtain a sufficient condition under which the unique extension of $T_1\otimes T_2$ to the complete $\epsilon$-tensor product is almost $r$-summing. \newline 1980 Mathematics Subject Classification: Primary 46E40. Secondary 47B10.

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