Abstract
The purpose of this paper is to answer the question posed by Feldman [9] on topological transitivity which states that "If E is transitive, does it follows that direct sum E ⊕ E is topologically transitive?" We will show that this question has a positive answer under certain conditions. In particular, we dene topologically transitive operators and use them to show that the direct sum E ⊕ E of two operators is topologically transitive whenever E is topologically transitive. Then, we give some examples of a topologically transitive operator which does not satisfy topologically transitive criterion and so not topologically transitive.
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