Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characterizations of all-derivable points in $B(H)$   Let ${\mathcal{K}}$ and ${\mathcal{H}}$ be two Hilbert space, and let
$B({\mathcal{K}},{\mathcal{H}})$ be the algebra of all bounded linear operators
from ${\mathcal{K}}$ into ${\mathcal{H}}$. We say that an element $G\in
B({\mathcal{H}},{\mathcal{H}})$ is an all-derivable point in
$B({\mathcal{H}},{\mathcal{H}})$ if every derivable linear mapping $\varphi$ at
$G$ (i.e. $\varphi(ST)=\varphi(S)T+S\varphi(T)$ for any $S,T\in B(H)$ with
$ST=G$) is a derivation. Let both $\varphi:
B({\mathcal{H}},{\mathcal{K}})\rightarrow B({\mathcal{H}},{\mathcal{K}})$ and
$\psi: B({\mathcal{K}},{\mathcal{H}})\rightarrow
B({\mathcal{K}},{\mathcal{H}})$ be two linear mappings. In this paper, the
following results will be proved : if $Y\varphi(W)=\psi(Y)W$ for any $Y\in
B({\mathcal{K}},{\mathcal{H}})$ and $W\in B({\mathcal{H}},{\mathcal{K}})$, then
$\varphi(W)=DW$ and $\psi(Y)=YD$ for some $D\in B({\mathcal{K}})$. As an
important application, we will show that an operator $G$ is an all-derivable
point in $B({\mathcal{H}},{\mathcal{H}})$ if and only if $G\neq 0$.

8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: eess
14
The categories of this paper are: math-ph
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The categories of this paper are: solv-int