Let X and Y be normed spaces. Then show that the following hold : (i) If Y is a Banach space, then BL(X,Y) is a Banach space. (ii) If X is a Banach space, then the quotient space X/Y is a Banach space.

Let X and Y be normed spaces. Then show that the following hold : (i) If Y is a Banach space, then BL(X,Y) is a Banach space. (ii) If X is a Banach space, then the quotient space X/Y is a Banach space.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.2: Vector Spaces

Problem 38E: Determine whether the set R2 with the operations (x1,y1)+(x2,y2)=(x1x2,y1y2) and c(x1,y1)=(cx1,cy1)...

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(a)
Let X and Y be normed spaces. Then show
that the following hold :
(i)
If Y is a Banach space, then BL(X,Y) is
a Banach space.
(ii) If X is a Banach space, then the
quotient space X/Y is a Banach space.
5.

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