The ideal of $p$-compact operators and its maximal hull
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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.References
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Additional Information
- Albrecht Pietsch
- Affiliation: Friedrich-Schiller-Universität Jena, Fakultät für Mathematik und Informatik, Ernst-Abbe-Platz 2, D-07743 Jena, Germany
- Address at time of publication: Biberweg 7, D-07749 Jena, Germany
- Email: a.pietsch@uni-jena.de
- Received by editor(s): July 11, 2011
- Received by editor(s) in revised form: March 4, 2012, and March 18, 2012
- Published electronically: October 17, 2013
- Communicated by: Marius Junge
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 142 (2014), 519-530
- MSC (2010): Primary 47B07, 47B10; Secondary 46B22, 47L20
- DOI: https://doi.org/10.1090/S0002-9939-2013-11758-2
- MathSciNet review: 3133993