Rank-one cross commutators on backward shift invariant subspaces on the bidisk |
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| Authors: | Kei Ji Izuchi Kou Hei Izuchi |
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| Affiliation: | (1) Department of Mathematics, Niigata University, Niigata 950-2181, Japan;(2) Graduate School of Science and Technology, Niigata University, Niigata 950-2181, Japan;(3) Department of Mathematics, Graduate School of Science, Hokkaido University, Sapporo 060-0810, Japan |
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| Abstract: | For a backward shift invariant subspace N in H 2(Γ2), the operators S z and S w on N are defined by S z = P N T z | N and S w = P N T w | N , where P N is the orthogonal projection from L 2(Γ2) onto N. We give a characterization of N satisfying rank [S z , S w *] = 1. The first author is partially supported by Grant-in-Aid for Scientific Research (No. 16340037), Japan Society for the Promotion of Science |
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| Keywords: | backward shift invariant subspace invariant subspace Hardy space cross commutator rank-one operator |
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