논문KCI 등재
Cross commutators on backward shift invariant subspaces over the bidisk II
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In the previous paper, we gave a characterization of backward shift invariant subspaces of the Hardy space over the bidisk on which [Szn; S w] = 0 for a positive integer n 2. In this case, it holds that Szn = cI for some c 2 C. In this paper, it is proved that if [Sφ; S w] = 0and φ 2 H1(z), then Sφ = cI for some c 2 C.
Abstract
In the previous paper, we gave a characterization of backward shift invariant subspaces of the Hardy space over the bidisk on which [Szn; S w] = 0 for a positive integer n 2. In this case, it holds that Szn = cI for some c 2 C. In this paper, it is proved that if [Sφ; S w] = 0and φ 2 H1(z), then Sφ = cI for some c 2 C.
참고문헌 (11)
- H. Bercovici, "Operator Theory and Arithmetic in H1, Mathematical Surveys and Mono- graphs" (1988), American Mathematical Society
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- X. Chen, "Analytic Hilbert Modules", pp.2003, Chapman & Hall
- K. J. Izuchi, "Commutativity in two variable Jordan blocks on the Hardy space"
- K. J. Izuchi, "Cross commutators on backward shift invariant subspaces over the bidisk", Acta Sci. Math. (Szeged), 72(1-2), pp.251~270 (2006)
- K. J. Izuchi, "Backward shift invariant subspaces in the bidisc. II", J. Operator Theory, 51(2), pp.361~376 (2004)
- K. J. Izuchi, "Backward shift invariant subspaces in the bidisc. III", Acta Sci. Math. (Szeged), 70(3-4), pp.727~749 (2004)
- V. Mandrekar, "The validity of Beurling theorems in polydiscs", Proc. Amer. Math. Soc, 103(1), pp.145~148 (1988)
- N. Nikol'skii, "Treatise on the Shift Operator" (1986), Springer-Verlag
- W. Rudin, "Function Theory in Polydiscs" (1969), Benjamin
- R. Schneider, "Isometries of Hp(Un)", Canad. J. Math, 25, pp.92~95 (1973)
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