報(bào)告題目：Irreducible approximation of Toeplitz operators and matrices
報(bào)告人：朱森教授
報(bào)告時(shí)間：2023.12.7 14：30-15：30
報(bào)告地點(diǎn)：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院 104報(bào)告廳
報(bào)告人簡(jiǎn)介：朱森，吉林大學(xué)數(shù)學(xué)學(xué)院教授，博士生導(dǎo)師.
主持國(guó)家自然科學(xué)基金青年、面上等項(xiàng)目. 近年來(lái)主要從事線(xiàn)性算子的復(fù)對(duì)稱(chēng)性、隨機(jī)理論等方面的研究，在 J. Funct. Anal., J.
London Math. Soc., Math. Ann., Math. Z, Sci. China Math., Trans.
AMS等雜志發(fā)表系列論文.
報(bào)告內(nèi)容簡(jiǎn)介：
The classification of the reducing subspaces of analytic Toeplitz operators on the classical Hardy space $H^2$ was completed in the 1970s due to work by Cowen and by Thomson. As for the reducing subspaces of non-analytic Toeplitz operators, to the best of our knowledge, there is no result in the literature so far.
We
initiate to describe the reducing subspaces of Toeplitz operators via
an approximation approach, showing that in the class of Toeplitz
operators with continuous symbols those irreducible ones constitute a
dense $G_\delta$. Our result depends on a finite-dimensional
approximation result, which asserts that in the class of $n\times n$
Toeplitz matrices those irreducible ones constitute an open dense
subset.
