The ideal of 𝑝-compact operators and its maximal hull

Pietsch, Albrecht

doi:10.1090/S0002-9939-2013-11758-2

The ideal of $p$-compact operators and its maximal hull
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Proc. Amer. Math. Soc. 142 (2014), 519-530 Request permission

Abstract:

Many recent papers have been devoted to the ideal of $p$-compact operators, denoted by $\mathfrak K_p$. In this note, we will revisit their main results by very simple proofs that are based on the general theory of operator ideals as developed in the author’s monograph more than 30 years ago. In several cases the outcome is even better. Moreover, the ideal of all operators with $p$-summing duals is identified as the maximal hull of $\mathfrak K_p$. As a byproduct, we show that $\mathfrak K_p^\textrm {max}$ is stable under the formation of projective tensor products.

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