Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Upper triangular operator matrices and stability of their various
  spectra   Denote by $T_n^d(A)$ an upper triangular operator matrix of dimension $n$
whose diagonal entries $D_i$ are known, where $A=(A_{ij})_{1\leq i<j\leq n}$ is
an unknown tuple of operators. This article is aimed at investigation of defect
spectrum
$\mathcal{D}^{\sigma_*}=\bigcup\limits_{i=1}^n\sigma_*(D_i)\setminus\sigma_*(T_n^d(A))$
, where $\sigma_*$ is a spectrum corresponding to various types of
invertibility: (left, right) invertibility, (left, right) Fredholm
invertibility, left Weyl invertibility, right Weyl invertibility. We give
characterizations for each of the previous types, and provide some sufficent
conditions for the stability of certain spectrum (case
$\mathcal{D}^{\sigma_*}=\emptyset$). Our main results hold for an arbitrary
dimension $n\geq2$ in arbitrary Hilbert or Banach spaces without assuming
separability, thus generalizing results from \cite{WU}, \cite{WU2}. Hence, we
complete a trilogy to previous work \cite{SARAJLIJA2}, \cite{SARAJLIJA3} of the
same author, whose goal was to explore basic invertibility properties of
$T_n^d(A)$ that are studied in Fredholm theory. We also retrieve a result from
\cite{BAI} in the case $n=2$, and we provide a precise form of the well known
'filling in holes' result from \cite{HAN}.

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The categories of this paper are: econ
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int