منابع مشابه
Uniqueness of Dilation Invariant Norms
Let δa be a nontrivial dilation. We show that every complete norm ‖ · ‖ on L1(RN ) that makes δa from (L1(RN ), ‖ · ‖) into itself continuous is equivalent to ‖ · ‖1. δa also determines the norm of both C0(R ) and Lp(RN ) with 1 < p < ∞ in a weaker sense. Furthermore, we show that even all the dilations do not determine the norm on L∞(RN ).
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2000
ISSN: 0022-1236
DOI: 10.1006/jfan.2000.3593