Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the extendability of some classes of maps on Hilbert $C^*$-modules   In this paper, we show that every completely semi-$\phi$-map on a submodule
of a Hilbert $C^*$-module has a completely semi-$\phi$-map extension on the
whole of module. We also investigate the extendability of $\phi$-maps and
provide examples of $\phi$-maps which has no $\phi$-map extension. Finally, we
introduce a category of Hilbert $C^*$-module and determine injective objects in
this category.

25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org