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2-Local real-linear isometries on C(1) ([0; 1])


Hironao Koshimizu
Takeshi Miura

Abstract

Let C(1)([0; 1]) be the Banach space of continuously differentiable functions on the closed unit interval [0; 1] equipped with the norm fα = lf(0)l+f, where g = sup{lg(t)l : t E [0; 1]g for g. If T : C (1)([0; 1]) →C(1)([0; 1]) is a 2-local real-linear isometry, then T is a surjective real-linear isometry.


 


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eISSN: 1727-933X
print ISSN: 1607-3606