학술저널
Isometries of a Subalgebra of C⁽¹⁾[0, 1]
- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 4, No. 1
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1991.0661 - 69 (9 pages)
- 0
By C⁽¹⁾[0, 1] we denote the Banach algebra of complex valued continuously differentiable functions on [0, 1] with norm given by ∥f∥=sup (│f(x)│+│f’(x)│) for f ∈ C⁽¹⁾. x∈[0,1] By A we denote the subalgebra of C⁽¹⁾ defined by A= {f ∈ C⁽¹⁾ : f(0) = f(1) and f’(0) = f’(1)}. By an isometry of A we mean a norm-preserving linear map of A onto itself. The purpose of this article is to describe the isometries of A. More precisely, we show tht any isometry of A is induced by a point map of the interval [0, 1) onto itself.
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