论文标题
高阶等距升降机和扩张
High order isometric liftings and dilations
论文作者
论文摘要
我们表明，Hilbert空间有限的线性运算符具有$ M $ iSometrict，对于某些整数$ M \ ge 1 $，并且仅当其权力的规范在多项式上生长。与宫缩统一扩张相比，我们证明了此类操作员还具有可逆的$ m $ isimetric扩张。我们还研究了售价运算符的$ 2 $ - 等级升降机和$ 3 $ iSometric-imoteric fiprings foguel-hankel操作员。
We show that a Hilbert space bounded linear operator has an $m$-isometric lifting for some integer $m\ge 1$ if and only if the norms of its powers grow polynomially. In analogy with unitary dilations of contractions, we prove that such operators also have an invertible $m$-isometric dilation. We also study $2$-isometric liftings of convex operators and $3$-isometric liftings of Foguel-Hankel operators.
