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Normed spaces have an algebraic structure of a vector space to which linear transformations are associated, and a topological structure of a metric space to which continuous functions are associated. Thus, the morphisms between normed spaces are functions that are simultaneously linear and continuous. Such functions are usually called continuous linear operators.

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Continuous Linear Operators

  • 章节

  • 发表日期：

    2025年

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  • Geraldo Botelho,
  • Daniel Pellegrino,
  • Eduardo Teixeira

摘要

Normed spaces have an algebraic structure of a vector space to which linear transformations are associated, and a topological structure of a metric space to which continuous functions are associated. Thus, the morphisms between normed spaces are functions that are simultaneously linear and continuous. Such functions are usually called continuous linear operators.