| 词条 | Operator space |
| 释义 |
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.".[1][2] The appropriate morphisms between operator spaces are completely bounded maps. Equivalent formulationsEquivalently, an operator space is a closed subspace of a C*-algebra. Category of operator spacesThe 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
References1. ^{{cite book |url=https://books.google.com/books?id=0pKL-o7WUOAC&pg=PA1&dq=Operator+space |title=Introduction to Operator Space Theory |last=Pisier |first=Gilles |publisher=Cambridge University Press |page=1 |isbn=978-0-521-81165-1 |year=2003 |accessdate=2008-12-18 }} 2. ^{{cite book |url=https://books.google.com/books?id=lwprbgvFA4IC&pg=PP11&dq=%22Operator+space%22 |title=Operator Algebras and Their Modules: An Operator Space Approach |authors=Blecher, David P. and Christian Le Merdy |publisher=Oxford University Press |page=First page of Preface |isbn=978-0-19-852659-9 |year=2004 |accessdate=2008-12-18 |nopp=true }} 2 : Banach spaces|Operator theory |
| 随便看 |
|
开放百科全书收录14589846条英语、德语、日语等多语种百科知识，基本涵盖了大多数领域的百科知识，是一部内容自由、开放的电子版国际百科全书。