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 ve&_eid=1-s2.0-S0022247X16304218&_mathId=si1.gif&_user=111111111&_pii=S0022247X16304218&_rdoc=1&_issn=0022247X&md5=503de5eaafe596503ff586ea0a6b0fc7">, where ve&_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∈C and ve&_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≠0. We also prove that the von Neumann algebra ve&_eid=1-s2.0-S0022247X16304218&_mathId=si4.gif&_user=111111111&_pii=S0022247X16304218&_rdoc=1&_issn=0022247X&md5=61e0ff5c977e232db32e9e723aa4147f"> is abelian.