Functional Analysis MCQs Quiz.2

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In this section, we are providing you with a functional analysis of multiple choice questions and their answers. All these available Functional analysis MCQs are collected from past university papers. These MCQ questions are also general in PDF format. Also, every student prepares for university exams manually.

Multiple Choice Question Section consists of MCQ tests. Each MCQs Test was prepared according to PPSC, FPSC, NTS, and other Examination preparation points of view. Some portions consist of only reading MCQs and some consist of online MCQs tests. After attempting the MCQs test You will get your score dashboard with their right and wrong answers. An explanation button will also be added for students’ concept clarifications.

Functional Analysis MCQs Quiz.2:

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Functional Analysis MCQs Quiz.2 With Answers

In the Functional Analysis MCQs Quiz, we are sharing Questions with you on Linear Operator, Bounded or unbounded linear operator, and Linear Functional Analysis MCQs questions to help us to increase our knowledge.

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1. Which of the following operator is bounded.

a) identity operator

b) zero operator

c) operator on a finite dimensional normed space

d) all of these

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2. If T : N → M is a bijective linear operator such that dim (N) = n and dim (M) = m, so

a) n≠m

b) n=m

c) n<m

d) n>m

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3. A linear operator T : N → M is bounded iff || T || is:

a) finite

b) infinite

c) closed

d) open

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4. A normed space N is a Banach space if N is:

a) finite dimensional

b) infinite dimensional

c) empty

d) compact

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5. If a linear functional f : N → F is bounded for all x ∈ N, then there exists k ≥ 0, such that

a) | f (x) | ≤ k

b) | f (x) | ≤ k||x||

c) | f (x) | ≤ ||x||

d) none

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6. The space of all bounded linear operator B (N, M) is Banach space if

a) N is Banach space

b) M is Banach space

c) N & M are Banach spaces

d) all of these

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7. The space of all bounded linear functional on a normed space is called:

a) algebraic dual space

b) dual space

c) conjugate space

d) all of these

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8. A linear operator T: N → M is bounded if there is a k > 0 such that for all x ∈ N,

a) || Tx || ≤ || kx ||

b) || Tx || ≤ k|| x ||

c) || Tx || ≤ || k ||

d) || Tx || = || k ||

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9. Let N be a finite-dimensional normed space, then N is isomorphic to

a) N* (first dual space)

b) N** (second dual space)

c) N*** (third dual space)

d) all of these

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10. If a linear functional f : N → F is continuous if

a) f is bounded

b) f is continuous at 0 ∈ N

c) ker f is clossed in N

d) all of these

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11. Let T: N → M be a linear operator then which of the following is correct.

a) T is continuous iff T is bounded

b) T is continuous iff T is continuous at 0 ∈ N

c) If T is continuous then ker T is closed in N

d) all of these

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12. If the range of a linear operator is the underlying field, the linear operator is called:

a) linear functional

b) linear function

c) linear transformation

d) all of these

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13. The inverse of a linear operator T exists if T is:

a) surjective

b) injective

c) bijective

d) symmetric

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14. Which of the following is a linear operator?

a) identity operator

b) differential operator

c) integral operator

d) all of these

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15. Let the dimension of a normed space N is n, then the dimension of its dual space N* is:

a) less than n

b) equal to n

c) greater then n

d) none

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