Kérchy László honlapja

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Cím:Isometries with isomorphic invariant subspace lattices.
Szerző:K\'erchy, L\'aszl\'o
Forrás:J. Funct. Anal. 170, No.2, 475-511 (2000)
Absztrakt:Summary: {\it J. B. Conway} and {\it T. A. Gillespie} [J. Funct. Anal. 64, 178-189 (1985; Zbl 0617.47002)] characterized those reductive normal operators which have isomorphic invariant subspace lattices. In a subsequent paper, {\it J. B. Conway} and {\it T. A. Gillespie} [J. Oper. Theory 22, 31-49 (1989; Zbl 0708.47005)] gave several necessary conditions for a map to be an isomorphism in the class of nonreductive isometries. In this paper, we provide a new necessary condition a bilateral shift. Furthermore, we give complete characterizations for the nonreductive components of the isometries to be cyclic. It turns out that this characterization is of a different type in the unitary and in the nonunitary case. We describe also when absolutely continuous unitary operators have spatially isomorphic invariant subspace lattices. Our results provide answers for questions posed in the second Conway and Gillespie paper referenced above. 
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