Geodesic
Multiplicative Isometries and Isometric Zero-Divisors
Canadian journal of mathematics, Tome 62 (2010) no. 5, pp. 961-974

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DOI

For some Banach spaces of analytic functions in the unit disk (weighted Bergman spaces, Bloch space, Dirichlet-type spaces), the isometric pointwise multipliers are found to be unimodular constants. As a consequence, it is shown that none of those spaces have isometric zero-divisors. Isometric coefficient multipliers are also investigated.
DOI : 10.4153/CJM-2010-048-7
Mots-clés : 30H05, 46E15, Banach spaces of analytic functions, Hardy spaces, Bergman spaces, Bloch space, Dirichlet space, Dirichlet-type spaces, pointwise multipliers, coefficient multipliers, isometries, isometric zerodivisors 
Aleman, Alexandru; Duren, Peter; Martín, María J.; Vukotić, Dragan. Multiplicative Isometries and Isometric Zero-Divisors. Canadian journal of mathematics, Tome 62 (2010) no. 5, pp. 961-974. doi: 10.4153/CJM-2010-048-7
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     title = {Multiplicative {Isometries} and {Isometric} {Zero-Divisors}},
     journal = {Canadian journal of mathematics},
     pages = {961--974},
     year = {2010},
     volume = {62},
     number = {5},
     doi = {10.4153/CJM-2010-048-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2010-048-7/}
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