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Multiplicative isometries on the Smirnov class

100%

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.

Real linear isometries between function algebras. II

100%

Hatori O., Miura T.

Open Mathematics

2013

tom 11

nr 10

1838-1842

We describe the general form of isometries between uniformly closed function algebras on locally compact Hausdorff spaces in a continuation of the study by Miura. We can actually obtain the form on the Shilov boundary, rather than just on the Choquet boundary. We also give an example showing that the form cannot be extended to the whole maximal ideal space.

Ograniczanie wyników

2 Open Mathematics

2 Hatori O.

1 Iida Y.

1 Miura T.

1 2013

1 2011

Wyniki wyszukiwania

Multiplicative isometries on the Smirnov class

Real linear isometries between function algebras. II