In functional analysis, a discipline within mathematics, an operator space is a Banach space "given together with an isometric embedding into the space B(H) of all bounded operators on a Hilbert space H.". Equivalently, an operator space is a closed subspace of a C*-algebra. The appropriate morphisms between operator spaces are completely bounded maps.
The category of operator spaces includes operator systems and operator algebras. For operator systems, in addition to a induced matrix norm of an operator space, one also has an induced matrix order. For operator algebras, there is still the additional ring structure.
- Pisier, Gilles (2003). Introduction to Operator Space Theory. Cambridge University Press. p. 1. ISBN 978-0-521-81165-1. Retrieved 2008-12-18.
- Blecher, David P. and Christian Le Merdy (2004). Operator Algebras and Their Modules: An Operator Space Approach. Oxford University Press. First page of Preface. ISBN 978-0-19-852659-9. Retrieved 2008-12-18.
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