In most of papers and classical text books, $p$-integral operators are defined and characterized by operators and commutative diagrams. This is quite different from $p$-summing operators and $p$-nuclear operators. I am wondering whether there are characterizations of $p$-integral operators by sequences such as weakly $p$-summable sequences, $p$-summable sequences.
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asked Oct 11, 2015 at 0:58
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$\begingroup$ I have not seen such a characterization and cannot imagine what could be one. $\endgroup$– Bill JohnsonCommented Oct 11, 2015 at 21:06
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$\begingroup$ This question may be stupid. It is well-known that on $l_{\infty}^{*}$, $weak^{*}$ convergent sequences are weakly convergent. Are there other spaces having this nice property besides $l_{\infty}$? Or what's the name of this property? $\endgroup$– Dongyang ChenCommented Oct 11, 2015 at 21:16
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$\begingroup$ A space having that property is called a Grothendieck space. Reflexive spaces and injective spaces and combinations thereof are the standard examples. I don't think that there is any characterization of this class of spaces. $\endgroup$– Bill JohnsonCommented Oct 12, 2015 at 22:29
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