Finite codimensional linear isometries on spaces of differentiable and Lipschitz functions

• Autorzy: Hironao Koshimizu
• Języki publikacji: EN

Abstrakty

EN

We characterize finite codimensional linear isometries on two spaces, C (n)[0; 1] and Lip [0; 1], where C (n)[0; 1] is the Banach space of n-times continuously differentiable functions on [0; 1] and Lip [0; 1] is the Banach space of Lipschitz continuous functions on [0; 1]. We will see they are exactly surjective isometries. Also, we show that C (n)[0; 1] and Lip [0; 1] admit neither isometric shifts nor backward shifts.

Słowa kluczowe

EN

Linear isometry; Finite codimension; Continuously differentiable function; Lipschitz continuous function; The Banach-Stone theorem; Shift

Kategorie tematyczne

• 46E15: Banach spaces of continuous, differentiable or analytic functions
• 46B04: Isometric theory of Banach spaces

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 1
• Strony: 139-146

Daty

wydano

2011-02-01

online

2010-12-30

Twórcy

autor

Hironao Koshimizu

• Shinshu University

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-010-0082-8