Functional Analysis Important MCQs Quiz With Answers

1 Comment / Functional Analysis Important MCQs / By lernerusman

Functional Analysis of past papers MCQ with answers for upcoming university exams. All these questions are answered by university professors and Ph.D. students. Solve these MCQs type quizzes and get the highest grade in university exams. In this quiz, we will discuss bounded or unbounded spaces and dual spaces, which are more important for exams. Also, we are talking about Banach spaces, infinite dimensions spaces, Inner and Outer spaces, Normed spaces, Complete spaces, etc.

Functional Analysis MCQs Quiz.1

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Functional Analysis MCQs Quiz.1 with Answers

In the Functional Analysis MCQs Quiz, we are sharing Questions with you on Normad Space, Infinity Space, and Other Functional Analysis MCQs questions help us to increase our knowledge.

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1. Which of the following is a normed space over itself.

a. R

b. C

c. Q

d. a and b only

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2. A complete normed space is called:

a. metric space

b. complete space

c. Banach space

d. inner product space

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3. Which of the following is Banach space?

a. R^n

b. C^n

c. l^infinity

d. all of these

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4. Which of the following is convex.

a. subspace of a linear space

b. open ball in a normed space

c. Closed ball in a normed space

d. all of these

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5. If F is a real or complex field, then vector space V over F is called:

a. linear space

b. normed space

c. inner product space

d. functional space

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6. If N is a normed space over a field F, thus for some fixed a ∈ F, the function f_a: N → N is continuous, then f_a (x) =

a. a+y

b. a-y

c. ay

d. a/y

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7. Which of the following is not a Banach space?

a. l_p

b. R

c. C

d. Q

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8. Which of the following is a normed space.

a. R^n

b. C^n

c. l_p

d. all of these

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9. Let N is a normal space, then the range set of norm on N is:

a. R

b. C

c. R U {0}

d. N

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10. Every norm is:

a. continuous function

b. uniformly continuous function

c. differentiable function

d. integrable function

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11. Any two norms on a normed space defined same topology if the norms are:

a. equivalent

b. not equivalent

c. same

d. complete

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12. Every normed space is a metric space with a metric d : N × N → R defined by
d (x, y) =

a. ||x+y||

b. ||x-y||

c. ||xy||

d. ||x/y||

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13. Let N is a normed space in which every closed and bounded subset is compact then N is:

a. finite dimensional

b. infinite dimensional

c. Banach space

d. compact space

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14. If N is a normal space then which of the following is correct for all x, y, z ∈ N

a. ||x + y|| ≥ 0

b. ||x + y|| ≤ ||x|| + ||y||

c. ||x - y|| ≤ ||x|| + ||y||

d. all of these

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15. If N is a normed space and f: N × N → N is uniformly continuous then f (x, y) =

a. x+y

b. x-y

c. xy

d. x/y

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Functional Analysis MCQs Quiz.1

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