Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the unit sphere of positive operators   Given a C$^*$-algebra $A$, let $S(A^+)$ denote the set of those positive
elements in the unit sphere of $A$. Let $H_1$, $H_2,$ $H_3$ and $H_4$ be
complex Hilbert spaces, where $H_3$ and $H_4$ are infinite-dimensional and
separable. In this note we prove a variant of Tingley's problem by showing that
every surjective isometry $\Delta : S(B(H_1)^+)\to S(B(H_2)^+)$ or
(respectively, $\Delta : S(K(H_3)^+)\to S(K(H_4)^+)$) admits a unique extension
to a surjective complex linear isometry from $B(H_1)$ onto $B(H_2))$
(respectively, from $K(H_3)$ onto $B(H_4)$). This provides a positive answer to
a conjecture posed by G. Nagy [\emph{Publ. Math. Debrecen}, 2018].

35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom