A compact operator T such that $T^{2}=T$ is a finite rank operator
104097
An idempotent operator is compact if and only if it is of finite rank
52791
Invertibility of an operator $T$ if $\|I-T\|<1$
64353
Does the set of matrix commutators form a subspace?
30996
If $\langle Ta, a\rangle \in \mathbb{R}$ for all $a$ then $T$ is self-adjoint
118996
Prove that $T$ is an orthogonal projection
45071
Having the derivative be an operator
11558
How to show that the limit of compact operators in the operator norm topology is compact
8805
Bounded linear operators that commute with translation
61484
Continuously invertible operators
77891
$(U\circ T)^{*} = T^{*}\circ U^{*}$
74611
$\operatorname{Adj} (\mathbf I_n x-\mathbf A)$ when $\operatorname{rank}(\mathbf A)\le n-2$
17262
Bounded operator that does not attain its norm
119684
Is a contraction idempotent operator self-adjoint?
112024
Let $T:V → V$ be a linear transformation where $V$ is finite dimensional.
123505
how to prove vector norm equivalence in finite dimensional space($\mathbb{R}^{n}$)?
59803
Converse of Schur's Lemma in finite dimensional vector spaces
119775
Density of finite rank operator in compact operators on Hilbert spaces