Invariant subspaces having two side frames over the bidisk

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• 作者：Kei Ji Izuchi^a ; ¹ ; ^{izuchi@m.sc.niigata-u.ac.jp" class="auth_mail" title="E-mail the corresponding author} ; Kou Hei Izuchi^b ; ^{izuchi@yamaguchi-u.ac.jp" class="auth_mail" title="E-mail the corresponding author} ; Yuko Izuchi^c ; ^{yfd10198@nifty.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Hardy space over the bidisk ; Invariant subspace ; Two side frames ; Rigid frame ; INS-type ; Unitarily equivalent
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：15 April 2016
• 年：2016
• 卷：436
• 期：2
• 页码：1102-1120
• 全文大小：390 K

文摘

An invariant subspace M   of the Hardy space over the bidisk is said to have two side frames if class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X15011749&_mathId=si1.gif&_user=111111111&_pii=S0022247X15011749&_rdoc=1&_issn=0022247X&md5=f7a12cc6433d5ff78be591283f0f2163" title="Click to view the MathML source">M⊖zMclass="mathContainer hidden">class="mathCode">$M\ominus zM$ and class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X15011749&_mathId=si2.gif&_user=111111111&_pii=S0022247X15011749&_rdoc=1&_issn=0022247X&md5=0b52f00f7597e7fb66fe4914e08a438f" title="Click to view the MathML source">M⊖wMclass="mathContainer hidden">class="mathCode">$M\ominus wM$ contain nonzero class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X15011749&_mathId=si3.gif&_user=111111111&_pii=S0022247X15011749&_rdoc=1&_issn=0022247X&md5=03c61e3dc59ffc79afe1dfba0e2b845e" title="Click to view the MathML source">T_wclass="mathContainer hidden">class="mathCode">$T_w$ and class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X15011749&_mathId=si4.gif&_user=111111111&_pii=S0022247X15011749&_rdoc=1&_issn=0022247X&md5=1ae77992fd520fdb61a82f93a233669f" title="Click to view the MathML source">T_zclass="mathContainer hidden">class="mathCode">$T_z$ invariant subspaces, respectively. If one frame is in class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X15011749&_mathId=si5.gif&_user=111111111&_pii=S0022247X15011749&_rdoc=1&_issn=0022247X&md5=ae2d615663918db57b8ed9be20e0dbc8" title="Click to view the MathML source">H²(z)class="mathContainer hidden">class="mathCode">$H^2(z)$ and the other is in class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X15011749&_mathId=si6.gif&_user=111111111&_pii=S0022247X15011749&_rdoc=1&_issn=0022247X&md5=9feba85ed948bc56eb309604a8cc9c09" title="Click to view the MathML source">H²(w)class="mathContainer hidden">class="mathCode">$H^2(w)$, M is said to have two side rigid frames. We shall show an example of an invariant subspace having two side frames which is not unitarily equivalent to any one having two side rigid frames. We also give some sufficient conditions on M for M to be unitarily equivalent to a rigid one.