Mathematics · Functional Analysis
Let T : X → Y be a bounded linear operator from a Banach space X to another Banach space Y. Which of the following conditions implies that T has a bounded inverse?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1inf||x||=1 ||Tx|| > 0 and T(X) is dense in Y✓
- 2inf||x||=1 ||Tx|| > 0
- 3inf||x||=1 ||Tx|| = 0 and T(X) is dense in Y
- 4inf||x||=1 ||Tx|| = 0
Correct answer
inf||x||=1 ||Tx|| > 0 and T(X) is dense in Y
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