Reducing subspaces for a class of non-analytic Toeplitz operators on the bidisk

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• 作者：Jia Deng^a ; ^{dj19891208@mail.dlut.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Yufeng Lu^a ; ^{lyfdlut@dlut.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Yanyue Shi^b ; ^{shiyanyue@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Reducing subspace ; Toeplitz operator ; Bergman space ; Polydisk
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：445
• 期：1
• 页码：784-796
• 全文大小：377 K

文摘

In this paper, we completely characterize all the reducing subspaces for a class of non-analytic Toeplitz operators with symbol class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16304218&_mathId=si1.gif&_user=111111111&_pii=S0022247X16304218&_rdoc=1&_issn=0022247X&md5=503de5eaafe596503ff586ea0a6b0fc7">class="imgLazyJSB inlineImage" height="19" width="145" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0022247X16304218-si1.gif">class="mathContainer hidden">class="mathCode">$\phi (z,w)=\alpha z^k+\beta {\bar{w}}^l$, where class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16304218&_mathId=si2.gif&_user=111111111&_pii=S0022247X16304218&_rdoc=1&_issn=0022247X&md5=cc80a32e52b77716de5a7687d178cafc" title="Click to view the MathML source">α,β∈Cclass="mathContainer hidden">class="mathCode">$\alpha ,\beta \in \mathbb{C}$ and class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16304218&_mathId=si3.gif&_user=111111111&_pii=S0022247X16304218&_rdoc=1&_issn=0022247X&md5=3bd025a7b49fcc73673d55ef518facf6" title="Click to view the MathML source">αβ≠0class="mathContainer hidden">class="mathCode">$\alpha \beta \ne 0$. We also prove that the von Neumann algebra class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16304218&_mathId=si4.gif&_user=111111111&_pii=S0022247X16304218&_rdoc=1&_issn=0022247X&md5=61e0ff5c977e232db32e9e723aa4147f">class="imgLazyJSB inlineImage" height="20" width="130" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0022247X16304218-si4.gif">class="mathContainer hidden">class="mathCode">${\mathcal{V}}^{⁎}(\phi )={\{T_{\phi },T_{\phi }^{⁎}\}}^{\prime }$ is abelian.