# Help me prove a lemma [closed]

Lemma: If $T\in\mathcal{G_p}$, then

$a)$ there exists a sequence $\{ T_{n}\}$ of finite-rank operators such that

$$\{\Vert T-T_{n}\Vert\}\rightarrow 0$$ and
$$\{{\vert T-T_{n}\vert}_{p}\}\rightarrow 0.$$

$b)$ for each bounded operators $A$ the operators $AT$ and $TA$ are in $\mathcal {G_{p}}$, and

$${\vert AT \vert}_{p}\leqq \Vert A \Vert {\vert T \vert}_{p},$$

$${\vert TA \vert}_{p}\leqq \Vert A \Vert {\vert T \vert}_{p}$$

-
Could you please explain what $\mathcal{G_p}$ stands for? –  23rd Dec 20 '12 at 19:37
My guess would be compact operators. If so just use projections of the main operator. –  toypajme Dec 20 '12 at 21:30
Could the OP edit the title for this question please so as to give more detail about the content of the question. –  Daniel Rust Dec 21 '12 at 16:59
I think $G_p$ is a Shatten $p$-class operartors. –  Norbert Dec 21 '12 at 19:30
@DanielRust: There is not even a question... –  Tomas Oct 21 '13 at 0:26
show 3 more comments

## closed as unclear what you're asking by 23rd, Cameron Buie, ncmathsadist, Tomas, Stefan4024Oct 21 '13 at 0:26

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, itâ€™s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question.If this question can be reworded to fit the rules in the help center, please edit the question.