How to show that there do not exist bounded operators $A$ and $B$ such that $AB-BA=I$
127121
The identity cannot be a commutator in a Banach algebra?
12189
Prove norm doesn't come from inner product.
44738
Compact operators on an infinite dimensional Banach space cannot be surjective
88349
Are the eigenvalues of $AB$ equal to the eigenvalues of $BA$? (Citation needed!)
38896
Prove that $A$ is bounded operator on $\ell^p$ and find $\| A\|$
95481
The set of self-adjoint operators over a Hilbert space doesn't form a lattice
81229
Show that $(C([a,b]),\|{\cdot}\|_2)$ is not a complete normed vector space
28819
A union of two subspaces not equal to the vector space.
78654
An example of a norm which can't be generated by an inner product
75117
$\mathrm{rank}(AB-BA)=1$ implies $A$ and $B$ are simultaneously triangularisable
90475
Coordinate-free proof of $\operatorname{Tr}(AB)=\operatorname{Tr}(BA)$?
11710
How to show that $\mathbb{Q}$ is not $G_\delta$
39466
Multiplication operator has no no eigenvalues
51302
Show that the operator norm is submultiplicative
99585
Do the non-zero eigenvalues of AB and BA have the same algebraic multiplicity (for AB and BA not square)?
158724
Show that $B$ is diagonalizable if If $AB=BA$ and $A$ has distinct real eigenvalues
81868
How to prove $\operatorname{Tr}(AB) = \operatorname{Tr}(BA)$?