Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Numerical radius and a notion of smoothness in the space of bounded
  linear operators   We observe that the classical notion of numerical radius gives rise to a
notion of smoothness in the space of bounded linear operators on certain Banach
spaces, whenever the numerical radius is a norm. We demonstrate an important
class of \emph{real} Banach space $ \mathbb{X} $ for which the numerical radius
defines a norm on $ \mathbb{L}(\mathbb{X}), $ the space of all bounded linear
operators on $ \mathbb{X} $. We characterize Birkhoff-James orthogonality in
the space of bounded linear operators on a finite-dimensional Banach space,
endowed with the numerical radius norm. Some examples are also discussed to
illustrate the geometric differences between the numerical radius norm and the
usual operator norm, from the viewpoint of operator smoothness.

8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga