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Let T be a closed linear operator with domain D(T) in a Banach space X and range R(T) in a normed space Y. If T^-1 exists and is bounded, show that R(T) is closed.

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Let T be a closed linear operator with domain D(T) in a Banach space X and range R(T) in a normed space Y. If T^-1 exists and is bounded, show that R(T) is closed.

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A closed linear operator and Banach space are investigated. The solution is detailed and well presented.

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Let T be a closed linear operator with domain in a Banach space X and range in a normed space Y. If exists and is ...

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