论文标题
关于具有连续符号的Toeplitz运营商的基本规范
On the essential norms of Toeplitz operators with continuous symbols
论文作者
论文摘要
众所周知，在Hardy Space $ H^P（\ Mathbb {T}）$，$ 1 <p <\ infty $大于或等于其符号的$ l^\ infty（\ mathbb {t}）$标准的基本规范。 1988年，A。Böttcher，N。Krupnik和B. Silbermann提出了一个问题，说明在连续符号的情况下，平等是否存在。我们以负面的方式回答这个问题。另一方面，我们表明，具有连续符号的toeplitz运算符的基本规范小于或等于符号的$ l^\ infty（\ mathbb {t}）$规范的两倍，并证明了更精确的$ p $依赖性估计。
It is well known that the essential norm of a Toeplitz operator on the Hardy space $H^p(\mathbb{T})$, $1 < p < \infty$ is greater than or equal to the $L^\infty(\mathbb{T})$ norm of its symbol. In 1988, A. Böttcher, N. Krupnik, and B. Silbermann posed a question on whether or not the equality holds in the case of continuous symbols. We answer this question in the negative. On the other hand, we show that the essential norm of a Toeplitz operator with a continuous symbol is less than or equal to twice the $L^\infty(\mathbb{T})$ norm of the symbol and prove more precise $p$-dependent estimates.
