scholarly journals Cyclic vectors and invariant subspaces for the backward shift operator

1970 ◽  
Vol 20 (1) ◽  
pp. 37-76 ◽  
Author(s):  
R. G. Douglas ◽  
H. S. Shapiro ◽  
A. L. Shields
Keyword(s):  
Shift Operator ◽  
Invariant Subspaces ◽  
Cyclic Vectors ◽  
Backward Shift

Imbedding theorems for the invariant subspaces of the backward shift operator

1988 ◽  
Vol 42 (2) ◽  
pp. 1562-1572 ◽  
Author(s):  
A. L. Vol'berg ◽  
S. R. Treil'
Keyword(s):  
Shift Operator ◽  
Invariant Subspaces ◽  
Backward Shift

Rank-one cross commutators on backward shift invariant subspaces on the bidisk

2009 ◽  
Vol 25 (5) ◽  
pp. 693-714 ◽  
Author(s):  
Kei Ji Izuchi ◽  
Kou Hei Izuchi
Keyword(s):  
Invariant Subspaces ◽  
Rank One ◽  
Backward Shift

scholarly journals The wandering subspace property and Shimorin’s condition of shift operator on the weighted Bergman spaces

2021 ◽  
Vol 16 (1) ◽  
Author(s):  
Changhui Wu ◽  
Zhijie Wang ◽  
Tao Yu
Keyword(s):  
Hardy Space ◽  
Toeplitz Operators ◽  
Shift Operator ◽  
Bergman Spaces ◽  
Invariant Subspaces ◽  
Weighted Bergman Spaces ◽  
Wandering Subspace ◽  
Formula Type

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 ) .

scholarly journals Closed commutants of the backward shift operator

1997 ◽  
Vol 179 (2) ◽  
pp. 371-396 ◽  
Author(s):  
Daniel Suárez
Keyword(s):  
Shift Operator ◽  
Backward Shift

scholarly journals CROSS COMMUTATORS ON BACKWARD SHIFT INVARIANT SUBSPACES OVER THE BIDISK II

2012 ◽  
Vol 49 (1) ◽  
pp. 139-151
Author(s):  
Kei Ji Izuchi ◽  
Kou Hei Izuchi
Keyword(s):  
Invariant Subspaces ◽  
Backward Shift

Ranks of backward shift invariant subspaces of the Hardy space over the bidisk

2012 ◽  
Vol 274 (3-4) ◽  
pp. 885-903 ◽  
Author(s):  
Kei Ji Izuchi ◽  
Kou Hei Izuchi ◽  
Yuko Izuchi
Keyword(s):  
Hardy Space ◽  
Invariant Subspaces ◽  
Backward Shift
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