Compact, non-nuclear operators
نویسندگان
چکیده
منابع مشابه
Representing non–weakly compact operators
For each S ∈ L(E) (with E a Banach space) the operator R(S) ∈ L(E/E) is defined by R(S)(x + E) = Sx + E (x ∈ E). We study mapping properties of the correspondence S → R(S), which provides a representation R of the weak Calkin algebra L(E)/W (E) (here W (E) denotes the weakly compact operators on E). Our results display strongly varying behaviour of R. For instance, there are no non–zero compact...
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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: Studia Mathematica
سال: 1974
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm-51-1-81-85