Set of surjective bounded linear operator between two Banach spaces is open.
15418
Why is the space of surjective operators open?
62999
Linear functional on a Banach space is discontinuous then its nullspace is dense.
125776
If space of bounded operators L(V,W) is Banach, V nonzero, then W is Banach (note direction of implication)
44738
Compact operators on an infinite dimensional Banach space cannot be surjective
8314
I am trying to find a Banach Space X and a singular operator (Infinite Dimensional Space)
78082
Dense subset of two Banach spaces also dense in the intersection
134492
Proving that a Hölder space is a Banach space
64840
A Banach space that is not a Hilbert space
83054
Let $E$ be a Banach space, prove that the sum of two closed subspaces is closed if one is finite dimensional
70264
Prove that the inverse image of an open set is open
51177
When are two norms equivalent on a Banach space?
97158
Prove that the operator norm is a norm
112231
Showing that a one-to-one linear transformation maps a linearly independent set onto a linearly independent set
8334
A reflexive Banach space is separable iff its dual is separable
121079
lemma: Cauchy sequences are bounded.
117502
Proving that a certain continuous function is surjective.
71848
Show that $(L^{p},\|\|_{p})$ is a Banach space.