Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some inequalities for $(\alpha, \beta)$-normal operators in Hilbert
  spaces   An operator $T$ acting on a Hilbert space is called $(\alpha ,\beta)$-normal
($0\leq \alpha \leq 1\leq \beta $) if \begin{equation*} \alpha ^{2}T^{\ast
}T\leq TT^{\ast}\leq \beta ^{2}T^{\ast}T. \end{equation*} In this paper we
establish various inequalities between the operator norm and its numerical
radius of $(\alpha ,\beta)$-normal operators in Hilbert spaces. For this
purpose, we employ some classical inequalities for vectors in inner product
spaces.

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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph