L(V,W) is Banach, then W is Banach
125776
If space of bounded operators L(V,W) is Banach, V nonzero, then W is Banach (note direction of implication)
90435
Prove that there exist linear functionals $L_1, L_2$ on $X$
43197
Showing that two definitions of $\limsup$ are equivalent
100161
Is it true that $\dim(X) \leq \dim(X^{\ast})$ for every infinite dimentional Banach space $X$?
63285
Prove that this space is not Banach
20467
Show that $(y_n)\in l^q$
109498
Linear maps $f: M_n \longrightarrow \mathbb{R}$ such that $f(AB) = f(BA)$
124786
Prove that V contains a subspace of each dimension
31686
Every metric space can be isometrically embedded in a Banach space, so that it's a linearly independent set
15300
How to show that $(W^\bot)^\bot=W$ (in a finite dimensional vector space)
67283
Is $L^{p}$ space with alternate norm Banach?
95513
Proving $W$ is a subspace of $P_{2}$
85239
Proof $dim(W)=dim(V)=n \implies W=V$
104302
Proving Geometric Hahn-Banach Implies Analytic Hahn-Banach
144112
Show that $c_0$ is a Banach space with the norm $\rVert \cdot \lVert_\infty$
26112
Inclusion of $l^p$ space for sequences
118272
Show that $L^1$ is strictly contained in $(L^\infty)^*$