Smallest closed subspace of $A$ in pre-Hilbert spaces
21459
Orthogonal complement examples
135650
Sequences in Hilbert spaces
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
90525
The subspace of $\ell_2$
10247
What is the minimum $ \sigma$-algebra that contains open intervals with rational endpoints
147914
Closed image of locally compact space
83360
The completion of a separable inner product space is a separable Hilbert space
105988
Find the uniform lower bound of the smallest eigenvalue of a certain matrix
70543
Does an uncountable discrete subspace of the reals exist?
59531
Do $T$-invariant subspaces necessarily have a $T$-invariant complement?
60684
Determine whether the set $W$ is a subspace in $\mathbb{R}^{3}$
136909
Functional Analysis: The rank of an operator detemines if it's a compact operator.
65963
Dense sets in Hilbert space of square summable sequences?
145668
Subspaces of $\ell^{2}$ and $\ell^{\infty}$ which are not closed?
12212
Showing a certain subspace of Hilbert space is dense
50946
Separable Hilbert space have a countable orthonormal basis