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We introduce now the definition of a mapping ideal, the operator space version of Banach operator ideals defined by Pietsch and also widely developed by Defant and Floret. The notion in our framework comes from Effros and Ruan (Operator Spaces. London Mathematical Society Monographs. New Series, vol. 23. The Clarendon Press Oxford University Press, New York, 2000, Sec. 12.2), though we have to strengthen Effros and Ruan’s definition in order to keep the essence of the traditional Banach space concept and allow the natural relationship with tensor norms. As in Defant and Floret (Tensor Norms and Operator Ideals. North-Holland Mathematics Studies, vol. 176. North-Holland Publishing Co., Amsterdam, 1993) the definition of ideal is restricted to the category of complete spaces.

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Mapping Ideals

  • 章节

  • 发表日期：

    2025年

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

摘要

We introduce now the definition of a mapping ideal, the operator space version of Banach operator ideals defined by Pietsch and also widely developed by Defant and Floret. The notion in our framework comes from Effros and Ruan (Operator Spaces. London Mathematical Society Monographs. New Series, vol. 23. The Clarendon Press Oxford University Press, New York, 2000, Sec. 12.2), though we have to strengthen Effros and Ruan’s definition in order to keep the essence of the traditional Banach space concept and allow the natural relationship with tensor norms. As in Defant and Floret (Tensor Norms and Operator Ideals. North-Holland Mathematics Studies, vol. 176. North-Holland Publishing Co., Amsterdam, 1993) the definition of ideal is restricted to the category of complete spaces.