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Finite codimensional linear isometries on spaces of differentiable and Lipschitz functions

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Koshimizu H.

Open Mathematics

2011

tom 9

nr 1

139-146

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.

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1 Open Mathematics

1 Koshimizu H.

1 2011

Wyniki wyszukiwania

Finite codimensional linear isometries on spaces of differentiable and Lipschitz functions