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1. CJM 2010 (vol 62 pp. 961)

Aleman, Alexandru; Duren, Peter; Martín, María J.; Vukotić, Dragan
Multiplicative Isometries and Isometric Zero-Divisors
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.

Keywords:Banach spaces of analytic functions, Hardy spaces, Bergman spaces, Bloch space, Dirichlet space, Dirichlet-type spaces, pointwise multipliers, coefficient multipliers, isometries, isometric zero-divisors
Categories:30H05, 46E15

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