The wandering subspace property and Shimorin’s condition of shift operator on the weighted Bergman spaces
Keyword(s):
AbstractIn the present paper, we first study the wandering subspace property of the shift operator on the $$I_{a}$$ I a type zero based invariant subspaces of the weighted Bergman spaces $$L_{a}^{2}(dA_{n})(n=0,2)$$ L a 2 ( d A n ) ( n = 0 , 2 ) via the spectrum of some Toeplitz operators on the Hardy space $$H^{2}$$ H 2 . Second, we give examples to show that Shimorin’s condition for the shift operator fails on the $$I_{a}$$ I a type zero based invariant subspaces of the weighted Bergman spaces $$L_{a}^{2}(dA_{\alpha })(\alpha >0)$$ L a 2 ( d A α ) ( α > 0 ) .
2010 ◽
Vol 26
(8)
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pp. 1567-1574
2013 ◽
Vol 76
(3)
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pp. 301-356
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1998 ◽
Vol 50
(3)
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pp. 658-672
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2008 ◽
Vol 348
(1)
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pp. 1-11
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