Functional Analysis ( Normed Linear Space )
76 videos • 6,126 views • by billionaire icon
1
Definition of Normed Linear Space @billionaireicon3311
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Real Space is a Normed Linear Space @billionaireicon3311
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Complex Space is a Normed Linear Space @billionaireicon3311
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Normed linear space and semi normed linear space with example
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Every normed linear space is a metric space, NLS @billionaireicon3311
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some properties of metric induced by norm, NLS @billionaireicon3311
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important property of a Normed Linear Space @billionaireicon3311
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Every metric is not a normed linear space | by Sapna | Normed Linear Space
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examples of metric spaces that are not obtained from norm, normed linear space
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definition of Convergent and Cauchy Sequence, Normed Linear Space
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Every convergent sequence is a cauchy sequence, Normed Linear Space
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Every cauchy sequence having convergent subsequence is convergent, Normed Linear Space |by Sapna|
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Norm, Addition and Scalar multiplication is continuous in a Normed Linear Space | by Sapna |
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Definition of Banach Space and Subspace of Banach Space, Normed Linear Space | by Sapna |
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a subspace of banach space complete iff subspace is closed in banach space, NLS @billionaireicon3311
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Completeness of Quotient Space, Normed Linear Space @billionaireicon3311
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If B is banach space then B' is also a banach space , | by Sapna | @billionaireicon3311
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N is NLS and M having elements of N that has norm one then N is banach space iff M is complete
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An important property for Holder's Inequality | by Sapna | @billionaireicon3311
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An important property for Minkowski Inequality | by Sapna | @billionaireicon3311
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Holder's Inequality for finite sum , | by Sapna | @billionaireicon3311
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Holder's Inequality for infinite sum , | by Sapna | @billionaireicon3311
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23
Definition of L^p space | by Sapna | @billionaireicon3311
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Holder's Inequality for Lp space | by Sapna | @billionaireicon3311
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Minkowski Inequality for Lp space | by Sapna | @billionaireicon3311
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LP space is Normed Linear Space , | by Sapna | @billionaireicon3311
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Cauchy Inequality, Normed Linear Space | by Sapna | @billionaireicon3311
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Riesz Fisher Theorem , Normed Linear Space | by Sapna | @billionaireicon3311
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Set of all continuous functions is a banach space | by Sapna | @billionaireicon3311
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l infinity is a banach space | by Sapna | @billionaireicon3311
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Minkowski Inequality for finite Sum , | by Sapna | @billionaireicon3311
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Minkowski Inequality for infinite Sum | by Sapna | @billionaireicon3311
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33
Normed Linear Space theorem Linear Transformation is continuous, bounded | by Sapna |
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Equivalent Statement for boundedness and Continuity of Linear Transformations | by Sapna |
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LT T is continuous iff bounded , Normed Linear Space | by Sapna | @billionaireicon3311
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T is Continuous either at all points or no points of Domain | by Sapna | @billionaireicon3311
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T is bounded iff T maps bounded set to bounded, Normed Linear Space | by Sapna |
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Iff condition on existence and continuity of inverse of T | by Sapna | @billionaireicon3311
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Normal of continuous transformation with example | by Sapna | @billionaireicon3311
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Completeness of set of all bounded LT, Normed Linear Space | by Sapna | @billionaireicon3311
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Hahn Banach Theorem , Normed Linear Space | by Sapna | @billionaireicon3311
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Consequence 1 of Hahn Banach Theorem | by Sapna | @billionaireicon3311
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Consequence 2 of Hahn Banach Theorem | by Sapna | @billionaireicon3311
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Consequence 3 of Hahn Banach Theorem | by Sapna | @billionaireicon3311
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If and only if condition for functional to be identical, Normed Linear Space |by Sapna |
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LT defined on finite NLS is bounded, Normed Linear Space | by Sapna |@billionaireicon3311
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Product of two bounded LT is bounded | by Sapna |@billionaireicon3311
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Topological Isomorphic Definition, Normed Linear Space @billionaireicon3311
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If and only if condition for topological Isomorphic, Normed Linear Space | by Sapna |
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Reisz theorem for bounded linear functional on C[a,b] | by Sapna |
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Bidual or Conjugate Space of N, | by Sapna | @billionaireicon3311
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Imbedding Theorem, Normed Linear Space | by Sapna | @billionaireicon3311
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Reflexive Mapping, Normed Linear Space | by Sapna | @billionaireicon3311
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Result based on Reflexive Mapping, Normed Linear Space | by Sapna | @billionaireicon3311
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Uniform Boundedness Theorem | by Sapna | @billionaireicon3311
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Consequence of Uniform Boundedness Theorem | by Sapna |
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Every Normed Linear Space is dense subspace, | by Sapna |@billionaireicon3311
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Projection, Normed Linear Space | by Sapna |@billionaireicon3311
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Banach space direct sum of closed linear spaces, Normed Linear Space | by Sapna |
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Direct product of two Normed Linear Space is also Normed Linear Space | by Sapna |
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Projection Theorem, Normed Linear Space | by Sapna |@billionaireicon3311
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Direct product is Banach space, Normed Linear Space | by Sapna |@billionaireicon3311
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Definition of graph of T, | by Sapna |@billionaireicon3311
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Closed Graph Theorem, | by Sapna |@billionaireicon3311
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Definition of Closed Linear Transformation, | by Sapna |@billionaireicon3311
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A LT is closed iff it's graph is closed, | by Sapna |@billionaireicon3311
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Boundedness of LT implies closed linear transformation | by Sapna |@billionaireicon3311
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Inverse of T is also closed linear transformation, Normed Linear Space | by Sapna |
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Conditions under which subspace of domain is closed, Normed Linear Space | by Sapna |
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F-Riesz Lemma, functional analysis | by Sapna |@billionaireicon3311
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F-Riesz Theorem, functional analysis | by Sapna |@billionaireicon3311
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Definition of weak and strong convergence, existence of unique limit | by Sapna |
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Strong convergence implies weak convergence | by Sapna |@billionaireicon3311
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Strong convergence iff weak convergence, functional analysis | by Sapna |@billionaireicon3311
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Set of all bounded LT is complete in strong sense | by Sapna |
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Every weak cauchy sequence is bounded, Normed Linear Space | by Sapna |
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