Let $T\in B(H)$ be such that $\langle Tx,x \rangle = 0$ for all $x\in H$. Prove that $T=0$.
11715
Prove that if $\langle Tx,x\rangle =0$ for all $x \in X$, then $T = 0$
15908
Is it true that $\int_{a}^b h^2=0\implies h=0$?
153355
Given $S \in B(Y^{*}, X^{*})$, does there exist $T\in B(X,Y)$ such that $S=T^{*}$?
31919
What can we say about the inner product $\langle f(t),f'(t) \rangle$?
44843
What is the difference between $|0\rangle $ and $0$?
151721
Uhlmann's Theorem: proof of $\text{tr}(A^{\dagger} B) = \langle m | A \otimes B |m\rangle $
37537
Show that $det(A)=0$ for a Matrix $A$ Such That for $X=[2,3,4]^{T}$, $AX=0$
88971
An approximate eigenvalue for $ T \in B(X) $.
9143
Solve $u_{xx}-3u_{xt}-4u_{tt}=0$ where $u(x,0)=x^2$ and $u_t(x,0)=e^x$
30569
Prove that the only operator on $\mathbb{C}$ for which his inner product is zero is zero
74559
$A$ and $B$ are ideals of a ring ${R}$ such that $A\cap B=\{0\}$. Prove that $st=0$ for every $s\in A, t\in B$.
50266
In the following figure prove that: $AK||BC$
101861
How do you prove that $tr(B^{T} A )$ is a inner product?
34147
$\|u\|\leq \|u+av\| \Longrightarrow \langle u,v\rangle=0$
80212
Suppose that $X$ is a topological space and $x_0\in X$. Prove that $\widetilde{H_n}(X)=H_n(X,x_0)$ for all $n\geq 0$.
65395
Prove that if $\operatorname{rank}(T) = \operatorname{rank}(T^2)$ then $R(T) \cap N(T) = \{0\}$
128985
Show that $\langle x,y\rangle_A = \langle Ax,Ay\rangle$ is an inner product on $\mathbb R^n$