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Functional AnalysisQuestions & AnswersThis is questionnaire & Answer that covers after 40th lectures in the module and could be attempted after listening to 40th lectures.528

Sl.No Chapter Name English
1Metric Spaces with ExamplesDownload
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2Holder Inequality and Minkowski InequalityDownload
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3Various Concepts in a Metric SpaceDownload
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4Separable Metrics Spaces with ExamplesDownload
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5Convergence, Cauchy Sequence, CompletenessDownload
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6Examples of Complete and Incomplete Metric SpacesDownload
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7Completion of Metric Spaces + TutorialDownload
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8Vector Spaces with ExamplesDownload
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9Normed Spaces with ExamplesDownload
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10Banach Spaces and Schauder BasicDownload
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11Finite Dimensional Normed Spaces and SubspacesDownload
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12Compactness of Metric/Normed SpacesDownload
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13Linear Operators-definition and ExamplesDownload
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14Bounded Linear Operators in a Normed SpaceDownload
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15Bounded Linear Functionals in a Normed SpaceDownload
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16Concept of Algebraic Dual and Reflexive SpaceDownload
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17Dual Basis & Algebraic Reflexive SpaceDownload
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18Dual Spaces with ExamplesDownload
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19Tutorial - IDownload
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20Tutorial - IIDownload
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21Inner Product & Hilbert SpaceDownload
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22Further Properties of Inner Product SpacesDownload
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23Projection Theorem, Orthonormal Sets and SequencesDownload
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24Representation of Functionals on a Hilbert SpacesDownload
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25Hilbert Adjoint OperatorDownload
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26Self Adjoint, Unitary & Normal OperatorsDownload
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27Tutorial - IIIDownload
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28Annihilator in an IPSDownload
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29Total Orthonormal Sets And SequencesDownload
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30Partially Ordered Set and Zorns LemmaDownload
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31Hahn Banach Theorem for Real Vector SpacesDownload
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32Hahn Banach Theorem for Complex V.S. & Normed SpacesDownload
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33Baires Category & Uniform Boundedness TheoremsDownload
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34Open Mapping TheoremDownload
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35Closed Graph TheoremDownload
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36Adjoint OperatorDownload
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37Strong and Weak ConvergenceDownload
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38Convergence of Sequence of Operators and FunctionalsDownload
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39LP - SpaceDownload
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40 LP - Space (Contd.)Download
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2BengaliNot Available
3GujaratiNot Available
4HindiNot Available
5KannadaNot Available
6MalayalamNot Available
7MarathiNot Available
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