A subnormal weighted shift on a directed tree whose nth power has trivial domain

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• 作者：Piotr Budzyński^a ; ^{piotr.budzynski@ur.krakow.pl" class="auth_mail" title="E-mail the corresponding author} ; Zenon Jan Jabłoński^b ; ^{Zenon.Jablonski@im.uj.edu.pl" class="auth_mail" title="E-mail the corresponding author} ; Il Bong Jung^c ; ^{ibjung@knu.ac.kr" class="auth_mail" title="E-mail the corresponding author} ; Jan Stochel^b ; ^{Jan.Stochel@im.uj.edu.pl" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Subnormal operator ; Power of an operator ; Trivial domain ; Weighted shift on a directed tree ; Composition operator in an L2L2-space
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：1 March 2016
• 年：2016
• 卷：435
• 期：1
• 页码：302-314
• 全文大小：422 K

文摘

It is shown that for any positive integer n there exists a subnormal weighted shift on a directed tree whose n  th power is closed and densely defined while its class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X15009518&_mathId=si1.gif&_user=111111111&_pii=S0022247X15009518&_rdoc=1&_issn=0022247X&md5=50228f48a8756f20411b51dbd0d5604e" title="Click to view the MathML source">(n+1)class="mathContainer hidden">class="mathCode">$(n+1)$th power has trivial domain. Similar result for composition operators in class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X15009518&_mathId=si127.gif&_user=111111111&_pii=S0022247X15009518&_rdoc=1&_issn=0022247X&md5=d7b5f8fabb6072ae4a24f1ba8cf3e6a3" title="Click to view the MathML source">L²class="mathContainer hidden">class="mathCode">$L^2$-spaces is established.