T is not compact and orthonormal sequence
119831
bounded operator $T$ is not compact then there exists an orthonormal sequence $e_n$ and $d>0$ such that $\|T(e_n)\|>d$ for all $n\in\Bbb{N}$?
80735
Show that $C_0([a, b], \mathbb{R})$ is not $\sigma$-compact
5506
Perturbation property of Orthonormal basis for Hilbert space
79417
A "non-trivial" example of a Cauchy sequence that does not converge?
90074
Show that the sequence $1,2,3,4,5,6,7,8,9,1,0,1,1,1,2,1,3,1,4,1,5,1,6,1,7,1,8,1,9,2,0,2,1,\cdots$ isn't periodic
65180
A compact Hausdorff space that is not metrizable
28819
A union of two subspaces not equal to the vector space.
137180
Orthonormal basis with specific norm
34677
Sequence Converging to Supremum
20437
Closed surjection that does not preserve regularity
107399
A sequence and convergence
92497
Isometric Embedding of a separable Banach Space into $\ell^{\infty}$
93923
No surjective bounded linear map from $\ell^2(\mathbf{N})$ to $\ell^1(\mathbf{N})$
112008
Ordinal $\omega_1$ is not compact
72900
What is the best way to show that the exponential sequence doesn't uniformally converge on an unbounded interval
121198
$W^{1,1}(\mathbb{R}^n)$ is not compactly embedded in $L^1(\mathbb{R}^n)$?
78648
Find an orthonormal basis for the subspace of $\mathbb R^4$