Multiplicative isometries on the Smirnov class
Osamu Hatori ; Yasuo Iida
Open Mathematics, Tome 9 (2011), p. 1051-1056 / Harvested from The Polish Digital Mathematics Library
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We show that T is a surjective multiplicative (but not necessarily linear) isometry from the Smirnov class on the open unit disk, the ball, or the polydisk onto itself, if and only if there exists a holomorphic automorphism Φ such that T(f)=f ○ Φ for every class element f or T(f) = f∘ϕ¯¯ for every class element f, where the automorphism Φ is a unitary transformation in the case of the ball and Φ(z 1, ..., z n) = (λ1zi1,...,λnzin) for |λ j| = 1, 1 ≤ j ≤ n, and (i 1; ..., i n)is some permutation of the integers from 1through n in the case of the n-dimensional polydisk.

Publié le : 2011-01-01
EUDML-ID : urn:eudml:doc:269758 
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     author = {Osamu Hatori and Yasuo Iida},
     title = {Multiplicative isometries on the Smirnov class},
     journal = {Open Mathematics},
     volume = {9},
     year = {2011},
     pages = {1051-1056},
     zbl = {1264.30042},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0068-1}
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Osamu Hatori; Yasuo Iida. Multiplicative isometries on the Smirnov class. Open Mathematics, Tome 9 (2011) pp. 1051-1056. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0068-1/

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