If the bounded operators $X\to Y$ form a Banach space in the operator norm, is $Y$ necessarily Banach?
125776
If space of bounded operators L(V,W) is Banach, V nonzero, then W is Banach (note direction of implication)
38761
Is the $ L^{p}$$[0,1]$ norm continuous in p?
6955
A Banach space is reflexive if and only if its dual is reflexive
71682
Proving that $X$ is a Banach space iff convergence of $\sum\|x_n\|$ implies convergence of $\sum x_n$
97454
Find the value of $\alpha-\beta$ if $g(x,y)=\alpha x+\beta y$ is a Hahn-Banach extension of $f$
82355
When is the image of a linear operator (between Banach spaces) closed?
144656
Linear functional and a bounded norm
95481
The set of self-adjoint operators over a Hilbert space doesn't form a lattice
43826
Example to prove that $ C^1[0,1] $ is not a Banach space for the uniform norm?
59697
Is the boundary of the unit sphere in every normed vector space compact?
134136
Does weak convergence imply $L^2$-norm convergence?
52791
Invertibility of an operator $T$ if $\|I-T\|<1$
28731
Banach space in functional analysis
34173
Banach spaces and their unit sphere
132869
Show that any bounded linear functional on a normed linear space is continuous
63285
Prove that this space is not Banach
17262
Bounded operator that does not attain its norm