Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some remarks on derivations on the algebra of operators in Hilbert
  pro-C*-bimodules   Suppose $A$ is a pro-C*-algebra. Let $L_{A}(E)$ be the pro-C*-algebra of
adjointable operators on a Hilbert $A$-module $E$ and let $K_{A}(E)$ be the
closed two sided $*$-ideal of all compact operators on $E$. We prove that if
$E$ be a full Hilbert $A$-module, the innerness of derivations on $K_{A}(E)$
implies the innerness of derivations on $L_{A}(E)$. We show that if $A$ is a
commutative pro-C*-algebra and $E$ is a Hilbert $A$-bimodule then every
derivation on $K_{A}(E)$ is zero. Moreover, if $A$ is a commutative
$\sigma$-C*-algebra and $E$ is a Hilbert $A$-bimodule then every derivation on
$L_{A}(E)$ is zero, too.

18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
1
The categories of this paper are: cs