Why is the closed $\operatorname{im} T$ in the definition of Fredholm Operator redundant?
96452
Is the closedness of the image of a Fredholm operator implied by the finiteness of the codimension of its image?
69542
Why do the $n \times n$ non-singular matrices form an "open" set?
41026
How to prove and interpret $\operatorname{rank}(AB) \leq \operatorname{min}(\operatorname{rank}(A), \operatorname{rank}(B))$?
32606
Is the operator $T((x_1,x_2,...,x_n))=(x_1,\frac{x_2}2,\frac{x_3}3,...)$ on $\ell^2$ self-adjoint and unitary
24072
Intuitive explanation of why $\dim\operatorname{Im} T + \dim\operatorname{Ker} T = \dim V$
31919
What can we say about the inner product $\langle f(t),f'(t) \rangle$?
60990
Tricky operator identity: $[L^2,[L^2,\vec{r}]]=2 \hbar ^2 \{ L^2, \vec{r}\}$?
136909
Functional Analysis: The rank of an operator detemines if it's a compact operator.
95481
The set of self-adjoint operators over a Hilbert space doesn't form a lattice
90475
Coordinate-free proof of $\operatorname{Tr}(AB)=\operatorname{Tr}(BA)$?
71945
How to reduce circuit elements of a decomposed $C^2(U)$ operation?
103839
Proving that $T^{2} = T$ for a linear operator on $W$ implies that $V = \operatorname{Null} T \oplus \operatorname{Range} T$
1043
Image of $L=\{z\in\Bbb C \mid a\operatorname{Re}(z)+b\operatorname{Im}(z)+c=0; a^2+b^2\neq0; a,b,c\in \Bbb R \}$ under the function $e^z$
148824
Is associative binary operator closed on this subset?
52198
Why is every selfadjoint operator closed?
142782
Operator< and strict weak ordering
26896
Why can't $ i\hbar\frac{\partial}{\partial t}$ be considered the Hamiltonian operator?