Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Best Approximation in Numerical Radius   Let $X$ be a reflexive Banach space. In this paper we give a necessary and
sufficient condition for an operator $T\in \mathcal{K}(X)$ to have the best
approximation in numerical radius from the convex subset $\mathcal{U} \subset
\mathcal{K}(X),$ where $\mathcal{K}(X)$ denotes the set of all linear, compact
operators from $X$ into $X.$ We will also present an application to minimal
extensions with respect to the numerical radius. In particular some results on
best approximation in norm will be generalized to the case of the numerical
radius.

22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg