Structure theorem for $A$-compact operators
نویسندگان
چکیده
منابع مشابه
Structure Theorem for a -compact Operators
A contraction Tdefined on a complex Hilbert space is called Acompact if there exists a nonzero function/analytic in the open unit disc and continuous on the closed disc such that f( T) is a compact operator. In this paper, the factorization of / is used to obtain a structure theorem which describes the spectrum of T. Introduction. A bounded linear operator T on a complex Banach space X is calle...
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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: Proceedings of the American Mathematical Society
سال: 1976
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1976-0428087-7