Abstract
An operatorT onH is called strongly irreducible ifT is not similar to any reducible operators. In this paper, we shall say ‘yes’ to answer the following question raised by D. A. Herrero.
Given an operatorT with connected spectrum σ(T) and a positive number ɛ, can we find a compact operatorK with ∥K∥ < ɛ such thatT+K is strongly irreducible?
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Supported by National Natural Science Foundation of China(19901011), Mathematical Center of State Education Commission of China and 973 Project of China