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PDF-21.NORMEDVECTORSPACESExercise1.5.ShowthateveryvectorspaceVoveranarbitr PDF document

41NORMEDVECTORSPACESsoTvn0Supposethatcdoesnotholdthenforalln2Zthereexistsvn2VsuchthatkTvnkWnkvnkVClearlyvn60Nowletv0n1 nkvnkVvnThenkv0nkV1nandvn0butkTv0nkW1andTv0n60Corollary114

41.NORMEDVECTORSPACESsoTvn!0.Supposethat(c)doesnothold thenforalln2Z+thereexistsvn2VsuchthatkTvnkWnkvnkV.Clearlyvn6=0.Nowletv0n=1 nkvnkVvn:Thenkv0nkV=1=nandvn!0 butkTv0nkW1andTv0n6!0.Corollary1.14.

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21.NORMEDVECTORSPACESExercise1.5.ShowthateveryvectorspaceVoveranarbitr: Transcript

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