On some local spectral theory and bounded local resolvent of operator matrices

Abdelaziz Tajmouati; Abdeslam El Bakkali; Mohammed Karmouni

Mathematica Bohemica (2018)

  • Volume: 143, Issue: 2, page 113-122
  • ISSN: 0862-7959

Abstract

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We extend and generalize some results in local spectral theory for upper triangular operator matrices to upper triangular operator matrices with unbounded entries. Furthermore, we investigate the boundedness of the local resolvent function for operator matrices.

How to cite

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Tajmouati, Abdelaziz, El Bakkali, Abdeslam, and Karmouni, Mohammed. "On some local spectral theory and bounded local resolvent of operator matrices." Mathematica Bohemica 143.2 (2018): 113-122. <http://eudml.org/doc/294408>.

@article{Tajmouati2018,
abstract = {We extend and generalize some results in local spectral theory for upper triangular operator matrices to upper triangular operator matrices with unbounded entries. Furthermore, we investigate the boundedness of the local resolvent function for operator matrices.},
author = {Tajmouati, Abdelaziz, El Bakkali, Abdeslam, Karmouni, Mohammed},
journal = {Mathematica Bohemica},
keywords = {local resolvent function; single-valued extension property; operator matrix},
language = {eng},
number = {2},
pages = {113-122},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On some local spectral theory and bounded local resolvent of operator matrices},
url = {http://eudml.org/doc/294408},
volume = {143},
year = {2018},
}

TY - JOUR
AU - Tajmouati, Abdelaziz
AU - El Bakkali, Abdeslam
AU - Karmouni, Mohammed
TI - On some local spectral theory and bounded local resolvent of operator matrices
JO - Mathematica Bohemica
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 143
IS - 2
SP - 113
EP - 122
AB - We extend and generalize some results in local spectral theory for upper triangular operator matrices to upper triangular operator matrices with unbounded entries. Furthermore, we investigate the boundedness of the local resolvent function for operator matrices.
LA - eng
KW - local resolvent function; single-valued extension property; operator matrix
UR - http://eudml.org/doc/294408
ER -

References

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  1. Aiena, P., Trapani, C., Triolo, S., 10.2298/FIL1402263A, Filomat 28 (2014), 263-273. (2014) Zbl06704755MR3360003DOI10.2298/FIL1402263A
  2. Bai, Q., Huang, J., Chen, A., 10.1080/03081087.2015.1111290, Linear Multilinear Algebra 64 (2016), 1583-1594. (2016) Zbl06605447MR3503370DOI10.1080/03081087.2015.1111290
  3. Barraa, M., Boumazgour, M., 10.1090/S0002-9939-03-06862-X, Proc. Am. Math. Soc. 131 (2003), 3083-3088. (2003) Zbl1050.47005MR1993217DOI10.1090/S0002-9939-03-06862-X
  4. Benhida, C., Zerouali, E. H., Zguitti, H., 10.1090/S0002-9939-05-07812-3, Proc. Am. Math. Soc. 133 (2005), 3013-3020. (2005) Zbl1067.47005MR2159780DOI10.1090/S0002-9939-05-07812-3
  5. Bermudez, T., Gonzalez, M., 10.1007/BF01332488, Integral Equations Oper. Theory 34 (1999), 1-8. (1999) Zbl0931.47003MR1690283DOI10.1007/BF01332488
  6. Bračič, J., Müller, V., 10.1007/s00020-005-1402-4, Integral Equations Oper. Theory 55 (2006), 477-486. (2006) Zbl1113.47003MR2250159DOI10.1007/s00020-005-1402-4
  7. Du, H., Jin, P., 10.2307/2160273, Proc. Am. Math. Soc. 121 (1994), 761-766. (1994) Zbl0814.47016MR1185266DOI10.2307/2160273
  8. Elbjaoui, H., Zerouali, E. H., 10.1155/S0161171203012043, Int. J. Math. Math. Sci. 2003 (2003), 2667-2672. (2003) Zbl1060.47003MR2005905DOI10.1155/S0161171203012043
  9. Eschmeier, J., Prunaru, B., 10.1007/BF01270923, Integral Equations Oper. Theory 42 (2002), 461-471. (2002) Zbl1010.47006MR1885444DOI10.1007/BF01270923
  10. González, M., An example of a bounded local resolvent, Operator Theory, Operator Algebras and Related Topics. Proc. 16th Int. Conf. Operator Theory, Timişoara, 1996 Theta Found., Bucharest (1997), 159-162. (1997) Zbl0943.47002MR1728418
  11. Han, J. K., Lee, H. Y., Lee, W. Y., 10.1090/S0002-9939-99-04965-5, Proc. Am. Math. Soc. 128 (2000), 119-123. (2000) Zbl0944.47004MR1618686DOI10.1090/S0002-9939-99-04965-5
  12. Houimdi, M., Zguitti, H., Local spectral properties of a square matrix of operators, Acta Math. Vietnam 25 (2000), 137-144 (in French). (2000) Zbl0970.47003MR1770883
  13. Neumann, M. M., On local spectral properties of operators on Banach spaces, Int. Workshop on Operator Theory, Cefalù, Italy, 1997 (P. Aiena et al., eds.) Circolo Matematico di Palermo, Suppl. Rend. Circ. Mat. Palermo, (2) (1998), 15-25. (1998) Zbl0929.47001MR1710819
  14. Zerouali, E. H., Zguitti, H., 10.1016/j.jmaa.2005.12.065, J. Math. Anal. Appl. 324 (2006), 992-1005. (2006) Zbl1105.47006MR2265096DOI10.1016/j.jmaa.2005.12.065
  15. Zhong, W., Method of separation of variables and Hamiltonian system, Comput. Struct. Mech. Appl. 8 (1991), 229-240 (in Chinese). (1991) 

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