论文标题
有界和紧凑的Toeplitz+Hankel矩阵
Bounded and compact Toeplitz+Hankel matrices
论文作者
论文摘要
我们表明，无限的toeplitz + hankel矩阵$ t（φ） + h（ψ）$在$ \ ell^p（\ mathbb {n} _0）上生成一个有界的（紧凑型）运算符，并使用$ 1 \ leq p \ leq p \ leq \ leq \ leq \ infty $ if，并且仅在$ t（$ t（φ）$ t（$）上，我们还为作用于反身耐性空间的Toeplitz+Hankel操作员提供了类似的特征。在这两种情况下，我们都提供了类似于棕色 - 半体定理的Toeplitz+Hankel形式的有界算子的内在表征。此外，我们建立了对此类运营商的规范和基本规范的估计。
We show that an infinite Toeplitz+Hankel matrix $T(φ) + H(ψ)$ generates a bounded (compact) operator on $\ell^p(\mathbb{N}_0)$ with $1\leq p\leq \infty$ if and only if both $T(φ)$ and $H(ψ)$ are bounded (compact). We also give analogous characterizations for Toeplitz+Hankel operators acting on the reflexive Hardy spaces. In both cases, we provide an intrinsic characterization of bounded operators of Toeplitz+Hankel form similar to the Brown-Halmos theorem. In addition, we establish estimates for the norm and the essential norm of such operators.
