Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the adjoint of Hilbert space operators   In general, it is a non trivial task to determine the adjoint $S^*$ of an
unbounded operator $S$ acting between two Hilbert spaces. We provide necessary
and sufficient conditions for a given operator $T$ to be identical with $S^*$.
In our considerations, a central role is played by the operator matrix
$M_{S,T}=\left(\begin{array}{cc} I & -T\\ S & I\end{array}\right)$. Our
approach has several consequences such as characterizations of closed, normal,
skew- and selfadjoint, unitary and orthogonal projection operators in real or
complex Hilbert spaces. We also give a self-contained proof of the fact that
$T^*T$ always has a positive selfadjoint extension.

10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph