# Functional Analysis MCQs With Answers 2024

Students if you are looking for Functional Analysis MCQs With Answers if yes? then you reach the right place where you can easily find the Functional MCQs for the final term exams as well as midterm exams where students can easily complete their Functional Analysis exams preparation.

Students you know these are Functional Analysis Final Term MCQs for the virtual university and others all students who have this book MTH641 or not any student can easily get and read them online from our website and these mcqs are totally free for all students.

## Functional Analysis MCQs With Answers

1: In an Inner Product space say X, if the sequences {n} and {y} are Cauchy, then (xn, Yn) is-

necessarily a Cauchy Sequence in F
necessarily a Cauchy Sequence in X
not necessarily a Cauchy Sequence in F
not necessarily a Cauchy Sequence in X

2: Null space is also a

Linear functional.
Canonical mapping.
Vector space.
Metric space.

3: If T is a continuous linear operator from a normed space X to normed space Y, then Tis_

bounded as well provided that X and Y are finite-dimensional
bounded as well irrespective of the dimensions of X and Y
unbounded as well Irrespective of dimensions of X and Y
unbounded as well provided that X and Y are Infinite dimensional

4: The mapping; T: V→ V defined by T(v) = a + v, where v EV is linear if

a=0
a #0

5: If a sequence → in a normed space X, then for a bounded linear operator T

Txn
TxnTx

6: Dual space is

71
R
11
R

7: For n-dimensional vector space and its dual space we have

R(X) = X = n
D(X) = X’ = n
dim(X) C dim(X)
dim(X) = dim(X) = n

8: Since a bounded linear operator T from the normed space X to normed space Y is defined and given as; VED(T) > 0, such that ||T||||||, then ||T||

sup ||T||
ZED(T)
both sup ZED(T) sup RED(T) 70 and sup ||T|| ZED(T)
None of these

9: Dual space of a normed space is

functional.
Metric space.
Incomplete.
Banach space.

10: If T:c[0,1]-c[0,1], which is defined and given as; 7(x)={fo1k(t,T)x(t)dt: |x|<k,the such that ||Tx||sk||x|| →

T is a non-linear bounded
T is linear unbounded
T is linearly bounded
T is non-linear unbounded

11: Since a bounded linear operator T from the normed space X to normed space Y is defined and given as; VxED(T) k> 0, such that ||T|| ||||, then ||T|| = 0⇒

T = 0
€ (0)
B or D
k<0

12: The pair is called Banach space. (V.<…>)

Inner product space.
Metric space.
Complete space.

13: Let T: XY be a linear operator, then the restriction of T is expressed as

To:Y B, BCY
To: B-BBCX
Tn:X-B, BCY
Tn: B-Y, BCX

14: Let S and T be linear operators, we have

(ST) ST
(ST)-1=1
(ST) T-1S-1
(ST)-S-T-1

15: IFT: R2R is defined by T (x, y)-y-z, then T-1 (6)

((t,t-6):t}
{(6+t,t):t}
Both ((6+,t): ER} and {(t,t-6):t}
None of these

16: The dot product is a

operator.
Mapping.
Functional.
Function.

17: If T and Ty are equal operators defined on a normed space X, then for any z X.Tiz necessarily

r=0.
1

18: IfT: R2 R2 defined by T(x, y) = (y, -5x+4y), then T-1 (-2,7) =

(3,2)
(-3,2)
(3,-2)
T-1 (-2,7) = (3,2)