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<p>We continue our study of the mapping ideal of operator <i>p</i>-compact maps, previously introduced by the authors. Our approach embraces a more geometric perspective, delving into the interplay between operator <i>p</i>-compact mappings and matrix sets, specifically we provide a quantitative notion of operator <i>p</i>-compactness for the latter. In particular, we consider operator <i>p</i>-compactness in the bidual and its relation with this property in the original space. Also, we deepen our understanding of the connections between these mapping ideals and other significant ones (e.g., completely <i>p</i>-summing, completely <i>p</i>-nuclear).</p>

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Revisiting Operator p-Compact Mappings

  • 期刊论文

  • 发表日期：

    2025年6月5日

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  • Javier Alejandro Chávez-Domínguez,
  • Verónica Dimant,
  • Daniel Galicer

摘要

We continue our study of the mapping ideal of operator p-compact maps, previously introduced by the authors. Our approach embraces a more geometric perspective, delving into the interplay between operator p-compact mappings and matrix sets, specifically we provide a quantitative notion of operator p-compactness for the latter. In particular, we consider operator p-compactness in the bidual and its relation with this property in the original space. Also, we deepen our understanding of the connections between these mapping ideals and other significant ones (e.g., completely p-summing, completely p-nuclear).