the extension oPerator of Theore m 8.6Therefore Fis bounded in i(R)and also inSince F is bounded both in LOR) and in LilIR), it isSolve problem number 31we Prove that H has a CompPact closure in.Proof of (7)Letct H be the unit ball in wTd: Let P behe extension oPerator of Theore m 8.6and set F=P(H),so that H=F;"LE(I) (for atl 1<9 c00) bj apPlying Theorem 4-26-1,1Clearly, F is bounded in w(R), because1,1W CR)CH, C, for some Ć1,1W (R)(I) m.La (I) by using (5).Lounded in LLIR) forall ge[1,0) (Prdtem 31).Scanned with CamScanner

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Answered: Since, F is bounded both in LOR) and in…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.2: Mappings

Problem 11E: For the given f:ZZ, decide whether f is onto and whether it is one-to-one. Prove that your decisions...

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Since, F is bounded both in LOR) and in lIR), it is Latnded in LLIR) forall fe[1,0) (Prdtem 31).