Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the extension of surjective isometries whose domain is the unit
  sphere of a space of compact operators   We prove that every surjective isometry from the unit sphere of the space
$K(H),$ of all compact operators on an arbitrary complex Hilbert space $H$,
onto the unit sphere of an arbitrary real Banach space $Y$ can be extended to a
surjective real linear isometry from $K(H)$ onto $Y$. This is probably the
first example of an infinite dimensional non-commutative C$^*$-algebra
containing no unitaries and satisfying the Mazur--Ulam property. We also prove
that all compact C$^*$-algebras and all weakly compact JB$^*$-triples satisfy
the Mazur--Ulam property.

0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat