A note on preservation of spectra for two given operators

Carlos Carpintero; Alexander Gutiérrez; Ennis Rosas; José Sanabria

Mathematica Bohemica (2020)

  • Volume: 145, Issue: 2, page 113-126
  • ISSN: 0862-7959

Abstract

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We study the relationships between the spectra derived from Fredholm theory corresponding to two given bounded linear operators acting on the same space. The main goal of this paper is to obtain sufficient conditions for which the spectra derived from Fredholm theory and other parts of the spectra corresponding to two given operators are preserved. As an application of our results, we give conditions for which the above mentioned spectra corresponding to two multiplication operators acting on the space of functions of bounded p -variation in Wiener’s sense coincide. Additional illustrative results are given too.

How to cite

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Carpintero, Carlos, et al. "A note on preservation of spectra for two given operators." Mathematica Bohemica 145.2 (2020): 113-126. <http://eudml.org/doc/297409>.

@article{Carpintero2020,
abstract = {We study the relationships between the spectra derived from Fredholm theory corresponding to two given bounded linear operators acting on the same space. The main goal of this paper is to obtain sufficient conditions for which the spectra derived from Fredholm theory and other parts of the spectra corresponding to two given operators are preserved. As an application of our results, we give conditions for which the above mentioned spectra corresponding to two multiplication operators acting on the space of functions of bounded $p$-variation in Wiener’s sense coincide. Additional illustrative results are given too.},
author = {Carpintero, Carlos, Gutiérrez, Alexander, Rosas, Ennis, Sanabria, José},
journal = {Mathematica Bohemica},
keywords = {restriction of an operator; spectral property; semi-Fredholm spectra; multiplication operator},
language = {eng},
number = {2},
pages = {113-126},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A note on preservation of spectra for two given operators},
url = {http://eudml.org/doc/297409},
volume = {145},
year = {2020},
}

TY - JOUR
AU - Carpintero, Carlos
AU - Gutiérrez, Alexander
AU - Rosas, Ennis
AU - Sanabria, José
TI - A note on preservation of spectra for two given operators
JO - Mathematica Bohemica
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 145
IS - 2
SP - 113
EP - 126
AB - We study the relationships between the spectra derived from Fredholm theory corresponding to two given bounded linear operators acting on the same space. The main goal of this paper is to obtain sufficient conditions for which the spectra derived from Fredholm theory and other parts of the spectra corresponding to two given operators are preserved. As an application of our results, we give conditions for which the above mentioned spectra corresponding to two multiplication operators acting on the space of functions of bounded $p$-variation in Wiener’s sense coincide. Additional illustrative results are given too.
LA - eng
KW - restriction of an operator; spectral property; semi-Fredholm spectra; multiplication operator
UR - http://eudml.org/doc/297409
ER -

References

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  3. Aiena, P., Biondi, M. T., Carpintero, C., 10.1090/S0002-9939-08-09138-7, Proc. Am. Math. Soc. 136 (2008), 2839-2848. (2008) Zbl1142.47004MR2399049DOI10.1090/S0002-9939-08-09138-7
  4. Astudillo-Villaba, F. R., Castillo, R. E., Ramos-Fernández, J. C., 10.14321/realanalexch.42.2.0329, Real Anal. Exch. 42 (2017), 329-344. (2017) Zbl06870333MR3721805DOI10.14321/realanalexch.42.2.0329
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  6. Barnes, B. A., 10.1090/S0002-9939-06-08624-2, Proc. Am. Math. Soc. 135 (2007), 1735-1740. (2007) Zbl1124.47002MR2286083DOI10.1090/S0002-9939-06-08624-2
  7. Berkani, M., 10.1007/BF01236475, Integral Equations Oper. Theory 34 (1999), 244-249. (1999) Zbl0939.47010MR1694711DOI10.1007/BF01236475
  8. Berkani, M., Sarih, M., 10.1017/S0017089501030075, Glasg. Math. J. 43 (2001), 457-465. (2001) Zbl0995.47008MR1878588DOI10.1017/S0017089501030075
  9. Carpintero, C., Muñoz, D., Rosas, E., Sanabria, J., García, O., 10.1007/s00009-013-0369-7, Mediterr. J. Math. 11 (2014), 1215-1228. (2014) Zbl1331.47005MR3268818DOI10.1007/s00009-013-0369-7
  10. Finch, J. K., 10.2140/pjm.1975.58.61, Pac. J. Math. 58 (1975), 61-69. (1975) Zbl0315.47002MR0374985DOI10.2140/pjm.1975.58.61
  11. Heuser, H. G., Functional Analysis, A Wiley-Interscience Publication. John Wiley & Sons, Chichester (1982). (1982) Zbl0465.47001MR0640429

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