科研之友
微信
新浪微博
Facebook
分享链接
摘要
A real seminormed involutive algebra is a real associative algebra endowed with an involutive antiautomorphism * and a submultiplicative seminorm p with p(a*) = p(a) for . Then is an involutive subsemigroup. For the case where is unital, our main result asserts that a function , V a Hilbert space, is completely positive (defined suitably) if and only if it is positive definite and analytic for any locally convex topology for which is open. If is the enveloping C*-algebra of and is the c (0)-direct sum of the symmetric tensor powers , then the above two properties are equivalent to the existence of a factorization , where is linear completely positive and . We also obtain a suitable generalization to non-unital algebras. An important consequence of this result is a description of the unitary representations of the unitary group with bounded analytic extensions to in terms of representations of the C*-algebra .
- 出版日期2015-12
