论文标题
与自我伴侣或双重阳性操作员的单一等效性
On unitary equivalence to a self-adjoint or doubly-positive Hankel operator
论文作者
论文摘要
让$ a $为复杂的可分开的希尔伯特空间上的有界，注入性和自我接合线性操作员。我们证明有一个纯等轴测图，$ v $，因此$ av> 0 $ and $ a $相对于$ v $，即$ v^*a = av $，当时且仅当$ a $不可逆转。等距$ v $可以选择为同构至$ n \ in \ mathbb {n} \ cup \ { + \ { + \ fty \} $单侧移位的副本，如果$ a $ a $最多具有频谱多重性，最多$ n $。我们进一步表明，所有iSometries $ v $的集合，因此$ a $相对于$ v $，与$ a^{ - 1} $的所有闭合，对称限制的集合进行了两次射击。
Let $A$ be a bounded, injective and self-adjoint linear operator on a complex separable Hilbert space. We prove that there is a pure isometry, $V$, so that $AV>0$ and $A$ is Hankel with respect to $V$, i.e. $V^*A = AV$, if and only if $A$ is not invertible. The isometry $V$ can be chosen to be isomorphic to $N \in \mathbb{N} \cup \{ + \infty \}$ copies of the unilateral shift if $A$ has spectral multiplicity at most $N$. We further show that the set of all isometries, $V$, so that $A$ is Hankel with respect to $V$, are in bijection with the set of all closed, symmetric restrictions of $A^{-1}$.
