无界严格奇异算子

Indagationes Mathematicae (Proceedings) Pub Date : 1988-09-26 DOI:10.1016/S1385-7258(88)80004-0

R.W. Cross

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引用次数: 9

摘要

设D(T)∧X→Y是一个无界线性算子，其中X和Y是赋范空间。证明了如果Y是完全的，那么当且仅当T是连续严格奇异算子与无界有限秩算子的和时，T是严格奇异的。对于Y不完全的情况，构造了一个反例。

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Unbounded strictly singular operators

Let D(T)⊂X→Y be an unbounded linear operator where X and Y are normed spaces. It is shown that if Y is complete then T is strictly singular if and only if T is the sum of a continuous strictly singular operator and an unbounded finite rank operator. A counterexample is constructed for the case in which Y is not complete.

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Indagationes Mathematicae (Proceedings)

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