GATE MA 2021 Paper 1 — page 15

Questions 43–45 of 65. Imported answers require review unless explicitly marked reviewed.

Paper practice 65 questionsPage 15 of 22

Let

be the Hilbert space of real valued square integrable functions on

equipped with the norm

. Consider the subspace

. For

, define

. Then

Your answerChoose one option.

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Let

be the Banach space of real valued continuous functions on

equipped with the supremum norm. Define

Let

denote the range space of

. Consider the following statements: P:

is a bounded linear operator. Q:

exists and is bounded. Then

Your answerChoose one option.

both P and Q are TRUE

P is TRUE and Q is FALSE

P is FALSE and Q is TRUE

both P and Q are FALSE

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Let

be the sequence space equipped with the norm

. Consider the subspace

and the linear transformation

given by

for

. Then

Your answerChoose one option.

is closed but NOT bounded

is bounded

is neither closed nor bounded

exists and is an open map

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2021 · Paper 1