On variable-exponent sequence spaces, modular-preserving linear maps are shown to be a set map followed by coordinate-wise multiplication by a bounded sequence, while shift-like maps preserve the norm only when the exponent sequence is invariant under the shift.
Uniformly convex spaces
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Isometric Operators on Variable-Exponent Discrete Lebesgue Spaces
On variable-exponent sequence spaces, modular-preserving linear maps are shown to be a set map followed by coordinate-wise multiplication by a bounded sequence, while shift-like maps preserve the norm only when the exponent sequence is invariant under the shift.