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Multiplicative isometries on the Smirnov class

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Hatori O., Iida Y.

Open Mathematics

2011

tom 9

nr 5

1051-1056

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) = $\overline {f^\circ \bar \varphi } $ 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) = $(\lambda _1 z_{i_1 } ,...,\lambda _n z_{i_n } )$ 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.

Ograniczanie wyników

1 Open Mathematics

1 Hatori O.

1 Iida Y.

1 2011

Wyniki wyszukiwania

Multiplicative isometries on the Smirnov class