The uniform boundedness theorem and a boundedness principle
نویسندگان
چکیده
منابع مشابه
Uniform Boundedness Principle
The following two propositions are true: (1) For every sequence s1 of real numbers and for every real number r such that s1 is bounded and 0 ≤ r holds lim inf(r s1) = r · lim inf s1. (2) For every sequence s1 of real numbers and for every real number r such that s1 is bounded and 0 ≤ r holds lim sup(r s1) = r · lim sup s1. Let X be a real Banach space. One can verify that MetricSpaceNormX is co...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2012
ISSN: 0168-0072
DOI: 10.1016/j.apal.2011.12.027