Banach space is direct sum of closed subspaces. Do these subspaces become continuous embeddings?
42516
If every $x\in X$ is uniquely $x=y+z$ then $\|z\|+\|y\|\leq C\|x\|$
4319
Vector space can be written as direct sum of subspaces
109046
Is the complement of an open ball in a Banach space connected?
71001
Do continuous linear functions between Banach spaces extend?
15839
equivalent norms in Banach spaces of infinite dimension
18373
Can infinite-dimensional vector spaces be decomposed into direct sum of its subspaces?
84830
Vector space of infinite sequences in $\Bbb R$
97391
Prove that $(C^1[0,1], \|\cdot\|)$ is not a Banach space
46326
The space $C[a,b]$ with $\|f\|:=\int_a^b |f(x)|d(x)$ is a normed space but not a Banach space
93511
Prove that $C^1([a,b])$ with the $C^1$- norm is a Banach Space
69206
A finite-dimensional vector space cannot be covered by finitely many proper subspaces?
63608
Cauchy sequence in a normed space
31686
Every metric space can be isometrically embedded in a Banach space, so that it's a linearly independent set
134065
A question about an $n$-dimensional subspace of $\mathbb{F}^{S}$.
140472
Is the space $\mathbb{N}$ is a baire spaces ? yes/No
137067
For Banach space there is a compact topological space so that the Banach space is isometrically isomorphic with a closed subspace of $C(X)$.
71682
Proving that $X$ is a Banach space iff convergence of $\sum\|x_n\|$ implies convergence of $\sum x_n$