Let V and W be two Banach spaces and (Tn) a sequence in the space of bounded linearmaps from V to W. For each x E V, let (Tn (x)) converges to Tx. Prove that(a) T is a bounded linear operator,(b) ||T|| < lim,-+o inf ||Tn||, where || · || is a norm on the space of bounded linearmaps.

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Description: Let V and W be two Banach spaces and (Tn) a sequence in the space of bounded linearmaps from V to W. For each x E V, let (Tn (x)) converges to Tx. Prove that(a) T is a bounded linear operator,(b) ||T|| < lim,-+o inf ||Tn||, where || · || is a norm o

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Let V and W be two Banach spaces and (Tn) a sequence in the space of bounded linear maps from V to W. For each x E V, let (T,(x)) converges to Tx. Prove that (a) T is a bounded linear operator, (b) ||T|| < limn inf ||Tn||, where || · || is a norm on the space of bounded linear maps.

Let V and W be two Banach spaces and (Tn) a sequence in the space of bounded linear maps from V to W. For each x E V, let (T,(x)) converges to Tx. Prove that (a) T is a bounded linear operator, (b) ||T|| < limn inf ||Tn||, where || · || is a norm on the space of bounded linear maps.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.1: Polynomials Over A Ring

Problem 21E: Describe the kernel of epimorphism in Exercise 20. Consider the mapping :Z[ x ]Zk[ x ] defined by...

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