Multipliers and Isometries in     H  E  ∞ | Zendy

Cambern Michael | Zendy; Jarosz Krzysztof | Zendy

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Multipliers and Isometries in H E ∞

Author(s) -

Cambern Michael,

Jarosz Krzysztof

Publication year - 1990

Publication title -

bulletin of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.396

H-Index - 48

eISSN - 1469-2120

pISSN - 0024-6093

DOI - 10.1112/blms/22.5.463

Subject(s) - mathematics , isometry (riemannian geometry) , conformal map , banach space , bounded function , pure mathematics , unit (ring theory) , space (punctuation) , constant (computer programming) , unit sphere , mathematical analysis , linguistics , philosophy , mathematics education , computer science , programming language

Let E be a complex Banach space andH E ∞the space of bounded analytic functions on the unit disc to E . By means of a study of the multipliers onH E ∞it is shown that, if Mult( E ) = C , then every isometry T ofH E ∞is of the form ( TF )( z ) = T F(τ(z)), where τ is a conformal map of the disc and T is a constant isometry of E .

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