For a backward shift invariant subspace N in H^2（Г^2）, the operators Sz and Sw on N are defined by Sz = PNTz｜N and Sw, = PNTw｜N, where PN is the orthogonal projection from L^2（Г^2） onto N. We give a characteri...For a backward shift invariant subspace N in H^2（Г^2）, the operators Sz and Sw on N are defined by Sz = PNTz｜N and Sw, = PNTw｜N, where PN is the orthogonal projection from L^2（Г^2） onto N. We give a characterization of N satisfying rank [Sz, Sw^＊] = 1.展开更多
In this paper, we give a criterion of the absolutely Cesàro bounded weighted backward shift in spirit of the comparison method. Our approach is to construct the proper product of weight functions <img src=&quo...In this paper, we give a criterion of the absolutely Cesàro bounded weighted backward shift in spirit of the comparison method. Our approach is to construct the proper product of weight functions <img src="Edit_7232e0dc-07ab-41c5-8657-a49f0463b47c.bmp" alt="" />by the fraction of two monomials of the indexes, then we apply proper scaling to give Cesàro boundedness. In particular, we present a new example of non Cesàro bounded weighted backward shift on <img src="Edit_799dadb7-40ab-48f9-bae3-191378f96164.bmp" alt="" />.展开更多
基金supported by Grant-in-Aid for Scientific Research (No. 16340037)Japan Society for the Promotion of Science
文摘For a backward shift invariant subspace N in H^2（Г^2）, the operators Sz and Sw on N are defined by Sz = PNTz｜N and Sw, = PNTw｜N, where PN is the orthogonal projection from L^2（Г^2） onto N. We give a characterization of N satisfying rank [Sz, Sw^＊] = 1.
文摘In this paper, we give a criterion of the absolutely Cesàro bounded weighted backward shift in spirit of the comparison method. Our approach is to construct the proper product of weight functions <img src="Edit_7232e0dc-07ab-41c5-8657-a49f0463b47c.bmp" alt="" />by the fraction of two monomials of the indexes, then we apply proper scaling to give Cesàro boundedness. In particular, we present a new example of non Cesàro bounded weighted backward shift on <img src="Edit_799dadb7-40ab-48f9-bae3-191378f96164.bmp" alt="" />.
