Positive linear functional on ∗-algebras of unbounded operators
نویسندگان
چکیده
منابع مشابه
On a functional equation for symmetric linear operators on $C^{*}$ algebras
Let $A$ be a $C^{*}$ algebra, $T: Arightarrow A$ be a linear map which satisfies the functional equation $T(x)T(y)=T^{2}(xy),;;T(x^{*})=T(x)^{*} $. We prove that under each of the following conditions, $T$ must be the trivial map $T(x)=lambda x$ for some $lambda in mathbb{R}$: i) $A$ is a simple $C^{*}$-algebra. ii) $A$ is unital with trivial center and has a faithful trace such ...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1968
ISSN: 0022-247X
DOI: 10.1016/0022-247x(68)90175-3