Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral and polar decomposition in AW*-algebras   We show the possibility and the uniqueness of polar decomposition of elements
of arbitrary AW*-algebras inside them. We prove that spectral decomposition of
normal elements of normal AW*-algebras is possible and unique inside them. The
possibility of spectral decomposition of normal elements does not depend on the
normality of the AW*-algebra under consideration.

25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex