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On Equivalence and Linearization of Operator Matrix Functions with Unbounded Entries

Engström, Christian LU and Torshage, Axel (2017) In Integral Equations and Operator Theory 89(4). p.465-492
Abstract

In this paper we present equivalence results for several types of unbounded operator functions. A generalization of the concept equivalence after extension is introduced and used to prove equivalence and linearization for classes of unbounded operator functions. Further, we deduce methods of finding equivalences to operator matrix functions that utilizes equivalences of the entries. Finally, a method of finding equivalences and linearizations to a general case of operator matrix polynomials is presented.

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author
and
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Block operator matrices, Equivalence after extension, Operator functions, Spectrum
in
Integral Equations and Operator Theory
volume
89
issue
4
pages
28 pages
publisher
Springer
external identifiers
  • scopus:85034244330
ISSN
0378-620X
DOI
10.1007/s00020-017-2415-5
language
English
LU publication?
no
additional info
Funding Information: The authors gratefully acknowledge the support of the Swedish Research Council under Grant No. 621-2012-3863. We sincerely thank the reviewer for the insightful comments, which were invaluable when revising the manuscript. Publisher Copyright: © 2017, The Author(s).
id
d1d7d3e2-c9c7-49bd-b507-9efb7f9a0cc6
date added to LUP
2023-03-24 11:07:25
date last changed
2023-03-24 13:51:00
@article{d1d7d3e2-c9c7-49bd-b507-9efb7f9a0cc6,
  abstract     = {{<p>In this paper we present equivalence results for several types of unbounded operator functions. A generalization of the concept equivalence after extension is introduced and used to prove equivalence and linearization for classes of unbounded operator functions. Further, we deduce methods of finding equivalences to operator matrix functions that utilizes equivalences of the entries. Finally, a method of finding equivalences and linearizations to a general case of operator matrix polynomials is presented.</p>}},
  author       = {{Engström, Christian and Torshage, Axel}},
  issn         = {{0378-620X}},
  keywords     = {{Block operator matrices; Equivalence after extension; Operator functions; Spectrum}},
  language     = {{eng}},
  month        = {{12}},
  number       = {{4}},
  pages        = {{465--492}},
  publisher    = {{Springer}},
  series       = {{Integral Equations and Operator Theory}},
  title        = {{On Equivalence and Linearization of Operator Matrix Functions with Unbounded Entries}},
  url          = {{http://dx.doi.org/10.1007/s00020-017-2415-5}},
  doi          = {{10.1007/s00020-017-2415-5}},
  volume       = {{89}},
  year         = {{2017}},
}