Essential Norm of Composition Operators on Banach Spaces of Hölder Functions
Keyword(s):
Let(X,d)be a pointed compact metric space, let0<α<1, and letφ:X→Xbe a base point preserving Lipschitz map. We prove that the essential norm of the composition operatorCφinduced by the symbolφon the spaceslip0(X,dα)andLip0(X,dα)is given by the formula‖Cφ‖e=limt→0 sup0<d(x, y)<t(d(φ(x),φ(y))α/d(x,y)α)whenever the dual spacelip0(X,dα)∗has the approximation property. This happens in particular whenXis an infinite compact subset of a finite-dimensional normed linear space.
Keyword(s):
1999 ◽
Vol 42
(2)
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pp. 139-148
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2017 ◽
Vol 13
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pp. 123-134
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1977 ◽
Vol 16
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pp. 79-81
2019 ◽
Vol 101
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pp. 311-324
2015 ◽
Vol 39
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pp. 497-509
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