Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Metric operators, generalized hermiticity and lattices of Hilbert lpaces   A quasi-Hermitian operator is an operator that is similar to its adjoint in
some sense, via a metric operator, i.e., a strictly positive self-adjoint
operator. Whereas those metric operators are in general assumed to be bounded,
we analyze the structure generated by unbounded metric operators in a Hilbert
space. It turns out that such operators generate a canonical lattice of Hilbert
spaces, that is, the simplest case of a partial inner product space
(PIP-space). We introduce several generalizations of the notion of similarity
between operators, in particular, the notion of quasi-similarity, and we
explore to what extend they preserve spectral properties. Then we apply some of
the previous results to operators on a particular PIP-space, namely, a scale of
Hilbert spaces generated by a metric operator. Finally, motivated by the recent
developments of pseudo-Hermitian quantum mechanics, we reformulate the notion
of pseudo-Hermitian operators in the preceding formalism.

34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph