<abstract xmlns="http://www.w3.org/1999/xhtml">

In this paper, we investigate the limit points set of descent spectrum of upper triangular operator matrices <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_mjpaa-2022-0024_eq_001.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>M</mi></mrow><mi>C</mi></msub><mo>=</mo><mrow><mo>(</mo><mrow><mtable columnalign="left"><mtr columnalign="left"><mtd columnalign="left"><mi>A</mi></mtd><mtd columnalign="left"><mi>C</mi></mtd></mtr><mtr columnalign="left"><mtd columnalign="left"><mn>0</mn></mtd><mtd columnalign="left"><mi>B</mi></mtd></mtr></mtable></mrow><mo>)</mo></mrow></mrow></math>
<tex-math>{M_C} = \left( {\matrix{A \hfill &amp; C \hfill \cr 0 \hfill &amp; B \hfill \cr } } \right)</tex-math>
</alternatives>
</inline-formula>. We prove that <italic>acc</italic>(<italic>σdes</italic>(<italic>MC</italic>)) ∪ <italic>Waccσdes</italic> = <italic>acc</italic>(<italic>σdes</italic>(<italic>A</italic>)) ∪ <italic>acc</italic>(<italic>σdes</italic>(<italic>B</italic>)) where <italic>Waccσdes</italic> is the union of certain holes in <italic>acc</italic>(<italic>σdes</italic>(<italic>MC</italic>)), which happen to be subsets of <italic>acc</italic>(<italic>σasc</italic>(<italic>B</italic>)) ∩ <italic>acc</italic>(<italic>σdes</italic>(<italic>A</italic>)). Furthermore, several sufficient conditions for <italic>acc</italic>(<italic>σdes</italic>(<italic>MC</italic>)) = <italic>acc</italic>(<italic>σdes</italic>(<italic>A</italic>)) ∪ <italic>acc</italic>(<italic>σdes</italic>(<italic>B</italic>)) holds for every <italic>C</italic> ∈ ℬ(<italic>Y</italic>, <italic>X</italic>) are given.
</abstract>

In this paper, we investigate the limit points set of descent spectrum of upper triangular operator matrices 


MC=(AC0B)
{M_C} = \left( {\matrix{A \hfill & C \hfill  \cr 0 \hfill & B \hfill  \cr  } } \right)

. We prove that acc(σdes(MC)) ∪ Waccσdes = acc(σdes(A)) ∪ acc(σdes(B)) where Waccσdes is the union of certain holes in acc(σdes(MC)), which happen to be subsets of acc(σasc(B)) ∩ acc(σdes(A)). Furthermore, several sufficient conditions for acc(σdes(MC)) = acc(σdes(A)) ∪ acc(σdes(B)) holds for every C ∈ ℬ(Y, X) are given.

Limit points for descent spectrum of operator matrices

Moroccan Journal of Pure and Applied Analysis

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Limit points for descent spectrum of operator matrices"}

In this paper, we investigate the limit points set of descent spectrum of upper triangular operator matrices 


MC=(AC0B)
{M_C} = \left( {\matrix{A \hfill & C...

Limit points for descent spectrum of operator matrices

Pubblicato online: 11 ott 2022

Pagine: 358 - 363

Ricevuto: 14 mag 2022

Accettato: 24 set 2022

DOI: https://doi.org/10.2478/mjpaa-2022-0024

Parole chiave
Descent spectrum, Single-valued extension property, Operator matrices

© 2022 H. Boua et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Limit points for descent spectrum of operator matrices

Pubblicato online: 11 ott 2022

Pagine: 358 - 363

Ricevuto: 14 mag 2022

Accettato: 24 set 2022

DOI: https://doi.org/10.2478/mjpaa-2022-0024

Parole chiaveDescent spectrum, Single-valued extension property, Operator matrices

© 2022 H. Boua et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Parole chiave
Descent spectrum, Single-valued extension property, Operator matrices