Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral decomposition of normal absolutely minimum attaining operators   Let $T:H_1\rightarrow H_2$ be a bounded linear operator defined between
complex Hilbert spaces $H_1$ and $H_2$. We say $T$ to be \textit{minimum
attaining} if there exists a unit vector $x\in H_1$ such that $\|Tx\|=m(T)$,
where $m(T):=\inf{\{\|Tx\|:x\in H_1,\; \|x\|=1}\}$ is the \textit{minimum
modulus} of $T$. We say $T$ to be \textit{absolutely minimum attaining}
($\mathcal{AM}$-operators in short), if for any closed subspace $M$ of $H_1$
the restriction operator $T|_M:M\rightarrow H_2$ is minimum attaining.
  In this paper, we give a new characterization of positive absolutely minimum
attaining operators ($\mathcal{AM}$-operators, in short), in terms of its
essential spectrum. Using this we obtain a sufficient condition under which the
adjoint of an $\mathcal{AM}$-operator is $\mathcal{AM}$.
  We show that a paranormal absolutely minimum attaining operator is
hyponormal. Finally, we establish a spectral decomposition of normal absolutely
minimum attaining operators. In proving all these results we prove several
spectral results for paranormal operators. We illustrate our main result with
an example.

13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn