Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invertible completions of $n\times n$ upper triangular operator matrices
  via normed spaces enclosures   Let $T_n^d(A)$ be an upper triangular operator matrix of dimension $n$ with
given diagonal entries. We assume $T_n^d(A)$ acts on a direct topological sum
of Banach spaces, where tuple $A=(A_{ij})_{1\leq i<j\leq n}$ consists of
unknown operators defined on appropriate domains. We prove that regularity of
$T_n^d(A)$ can be characterized in terms of diagonal operators solely, and we
extend the well known result from \cite{HAN} and a recent result from
\cite{SARAJLIJADJ} from $n=2,3$ to arbitrary dimension $n$. Thus, invertibility
of upper triangular operator matrices is completely characterized, and the
answer to a question raised by the present author and D. S. Djordjevi\'c in
\cite{SARAJLIJADJ} is given. We obtain some perturbation and filling in holes
results as consequences.

10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph