Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Dirac operator of a commuting d-tuple   Given a commuting d-tuple $\bar T=(T_1,...,T_d)$ of otherwise arbitrary
nonnormal operators on a Hilbert space, there is an associated Dirac operator
$D_{\bar T}$. Significant attributes of the d-tuple are best expressed in terms
of $D_{\bar T}$, including the Taylor spectrum and the notion of Fredholmness.
  In fact, {\it all} properties of $\bar T$ derive from its Dirac operator. We
introduce a general notion of Dirac operator (in dimension $d=1,2,...$) that is
appropriate for multivariable operator theory. We show that every abstract
Dirac operator is associated with a commuting $d$-tuple, and that two Dirac
operators are isomorphic iff their associated operator $d$-tuples are unitarily
equivalent.
  By relating the curvature invariant introduced in a previous paper to the
index of a Dirac operator, we establish a stability result for the curvature
invariant for pure d-contractions of finite rank. It is shown that for the
subcategory of all such $\bar T$ which are a) Fredholm and and b) graded, the
curvature invariant $K(\bar T)$ is stable under compact perturbations. We do
not know if this stability persists when $\bar T$ is Fredholm but ungraded,
though there is concrete evidence that it does.

0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom