Functional analysis previous year question and answers
24 videos • 1,578 views • by msc mathematics
1
show that L(x, y) is a banach space
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2
show that a banach space X can be identified with a subspace of X**
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3
state and prove Riesz representation theorem
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4
prove that the intersection of convex sets is convex
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5
L⊕L⊥=H and (L⊥)⊥=H
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6
state and prove the integral form of Minkowski inequality
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7
show that Lp is a banach space
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8
show that for the shift operator A in l² A^n does not converge strongly to zero
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9
show that for a normed space X,X* is a total set
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10
state the Banach open theorem
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11
let H be an inner product space. show that H is also a normed space under the hilbertian norm
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12
state and prove cauchy scwartz inequality
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13
state and prove bessel's inequality
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14
state and prove condition for a hilbert space to be seperable
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15
state and prove Gram-schmidt orthogonalization theorem
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16
state the parseval formula in a hilbert space
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17
state and prove parseval's identity
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18
2021.4.state Hahn banach extension theorem
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19
All normed spaces are metric space
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20
state and prove parallellogram law
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21
if x° is a closed space of a linear space X then PT the quotient space X\X° is a normal space
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22
3.find the codimension of C° in c
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23
arzela's theorem with detailed explanation
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24
norm convergence, strong convergence, weak convergence
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