If $\langle Tv,v\rangle\in\mathbb{R}$, prove that $T$ is self-adjoint
30996
If $\langle Ta, a\rangle \in \mathbb{R}$ for all $a$ then $T$ is self-adjoint
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
2439
If a linear operator has an adjoint operator, it is bounded
125894
Prove that $\mathbb{Q}$ belongs to the Borel $\sigma$-algebra of $\mathbb{R}$
34147
$\|u\|\leq \|u+av\| \Longrightarrow \langle u,v\rangle=0$
27086
proof for $\langle q| p \rangle = e^{ipq}$
55067
Norm of self-adjoint operator
128361
The kernel and range of the powers of a self-adjoint operator
117688
Prove that $\def\Aut{\operatorname{Aut}}\Aut(\mathbf{Z_{n}})\simeq \mathbf{Z_{n}^{*}}$
99942
A normal, idempotent linear operator must be self-adjoint
6202
$V$ be a vector space , $T:V \to V$ be a linear operator , then is $\ker (T) \cap R(T) \cong R(T)/R(T^2) $?
146730
The adjoint of left exterior multiplication by $\xi$ for hodge star operator
127047
How to show that $\sum_{i=1}^n | \langle f, f_i\rangle |^2 \leq \Vert f \Vert^2$
73406
Prove that $E_{\lambda}(T)=E_{\lambda^{-1}}(T^{-1})$ if $T$ is an invertible linear operator on a finite dimensional vector space $V$
128917
Inner Product on $\mathbb{R}$ and on $\mathbb{C}$
66283
Let V be a vector space. If every subspace of V is T-invariant, prove that there exist a scalar multiple c such that T=c1v
82464
$U^*\otimes V$ versus $L(U,V)$ for infinite dimensional spaces