Complexity of Operators on Compact Sets
نویسندگان
چکیده
منابع مشابه
Compact Sets and Compact Operators
Proof. Properties 2 and 3 are left to the reader. For property 1, assume that S is an unbounded compact set. Since S is unbounded, we may select a sequence {vn}n=1 such that ‖vn‖ → 0 as n→∞. Since S is compact, this sequence will have a convergent subsequence, say {vk}k=1, which will still be unbounded. This sequence is Cauchy, so there is a positive integer K for which ‖v`− vm‖ ≤ 1/2 for all `...
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ژورنال
عنوان ژورنال: Electronic Notes in Theoretical Computer Science
سال: 2008
ISSN: 1571-0661
DOI: 10.1016/j.entcs.2008.03.011