In functional analysis, a discipline within mathematics, an '''operator space''' is a normed vector space (not necessarily a Banach space)<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 }}</ref> "given together with an isometric embedding into the space ''B(H)'' of all bounded operators on a Hilbert space ''H''.".<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 }}</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 }}</ref> The appropriate morphisms between operator spaces are completely bounded maps. ==Equivalent formulations== Equivalently, an operator space is a subspace of a C*-algebra.
==Category of operator spaces== The category of operator spaces includes operator systems and operator algebras. For operator systems, in addition to an induced matrix norm of an operator space, one also has an induced matrix order. For operator algebras, there is still the additional ring structure. ==See also== * Gilles Pisier * Operator system
== References == {{Reflist|2}}
{{Functional analysis}} {{SpectralTheory}}
Category:Banach spaces Category:Operator theory