查看“︁算子空间”︁的源代码

[[泛函分析]]中，'''算子空间'''（operator space）是[[赋范向量空间]]（不必是[[巴拿赫空间]]）<ref>{{cite book |url=https://books.google.com/books?id=VtSFHDABxMIC |title=Completely Bounded Maps and Operator Algebras |last=Paulsen |first=Vern |publisher=[[Cambridge University Press]] |page=26 |isbn=978-0-521-81669-4 |year=2002 |access-date=2022-03-08 |archive-date=2023-05-15 |archive-url=https://web.archive.org/web/20230515050640/https://books.google.com/books?id=VtSFHDABxMIC |dead-url=no }}</ref>，“与到[[希尔伯特空间]]''H''上所有[[有界算子]]空间<math>B(H)</math>的[[等距同构|等距]][[单射|嵌入]]一同给出”。<ref>{{cite book |url=https://books.google.com/books?id=0pKL-o7WUOAC&dq=Operator+space&pg=PA1 |title=Introduction to Operator Space Theory |last=Pisier |first=Gilles |publisher=[[Cambridge University Press]] |page=1 |isbn=978-0-521-81165-1 |year=2003 |access-date=2008-12-18 |archive-date=2023-05-15 |archive-url=https://web.archive.org/web/20230515051120/https://books.google.com/books?id=0pKL-o7WUOAC&dq=Operator+space&pg=PA1 |dead-url=no }}</ref><ref>{{cite book |url=https://books.google.com/books?id=lwprbgvFA4IC&dq=%22Operator+space%22&pg=PP11 |title=Operator Algebras and Their Modules: An Operator Space Approach |author1=Blecher, David P. |author2=Christian Le Merdy |publisher=[[Oxford University Press]] |page=First page of Preface |isbn=978-0-19-852659-9 |year=2004 |access-date=2008-12-18 |no-pp=true |archive-date=2024-04-05 |archive-url=https://web.archive.org/web/20240405092531/https://books.google.com/books?id=lwprbgvFA4IC&dq=%22Operator+space%22&pg=PP11 |dead-url=no }}</ref>算子空间之间的适当态射是完备有界映射。

==等价形式化==
等价地，算子空间是[[C*-代数]]的[[线性子空间|子空间]]。

==算子空间范畴==
算子空间[[范畴 (数学)|范畴]]包含[[算子系统]]与[[算子代数]]。对于算子系统，除了算子空间的诱导矩阵范数之外，还有诱导矩阵阶。对于算子代数，还有额外的[[环 (代数)|环]]结构。
== 参考文献 ==
{{Reflist|2}}

{{泛函分析}}

[[Category:巴拿赫空间]]
[[Category:算子理论]]