On some local spectral theory and bounded local resolvent of operator matrices
Mathematica Bohemica, Tome 143 (2018) no. 2, pp. 113-122
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
DOI : 10.21136/MB.2017.0052-16
Classification : 47A10, 47A11, 47A53
Keywords: local resolvent function; single-valued extension property; operator matrix
@article{10_21136_MB_2017_0052_16,
     author = {Tajmouati, Abdelaziz and El Bakkali, Abdeslam and Karmouni, Mohammed},
     title = {On some local spectral theory and bounded local resolvent of operator matrices},
     journal = {Mathematica Bohemica},
     pages = {113--122},
     year = {2018},
     volume = {143},
     number = {2},
     doi = {10.21136/MB.2017.0052-16},
     mrnumber = {3831481},
     zbl = {06890409},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2017.0052-16/}
}
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
SP  - 113
EP  - 122
VL  - 143
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2017.0052-16/
DO  - 10.21136/MB.2017.0052-16
LA  - en
ID  - 10_21136_MB_2017_0052_16
ER  - 
%0 Journal Article
%A Tajmouati, Abdelaziz
%A El Bakkali, Abdeslam
%A Karmouni, Mohammed
%T On some local spectral theory and bounded local resolvent of operator matrices
%J Mathematica Bohemica
%D 2018
%P 113-122
%V 143
%N 2
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2017.0052-16/
%R 10.21136/MB.2017.0052-16
%G en
%F 10_21136_MB_2017_0052_16
Tajmouati, Abdelaziz; El Bakkali, Abdeslam; Karmouni, Mohammed. On some local spectral theory and bounded local resolvent of operator matrices. Mathematica Bohemica, Tome 143 (2018) no. 2, pp. 113-122. doi: 10.21136/MB.2017.0052-16

[1] Aiena, P., Trapani, C., Triolo, S.: SVEP and local spectral radius formula for unbounded operators. Filomat 28 (2014), 263-273. | DOI | MR | JFM

[2] Bai, Q., Huang, J., Chen, A.: Essential, Weyl and Browder spectra of unbounded upper triangular operator matrices. Linear Multilinear Algebra 64 (2016), 1583-1594. | DOI | MR | JFM

[3] Barraa, M., Boumazgour, M.: A note on the spectrum of an upper triangular operator matrix. Proc. Am. Math. Soc. 131 (2003), 3083-3088. | DOI | MR | JFM

[4] Benhida, C., Zerouali, E. H., Zguitti, H.: Spectra of upper triangular operator matrices. Proc. Am. Math. Soc. 133 (2005), 3013-3020. | DOI | MR | JFM

[5] Bermudez, T., Gonzalez, M.: On the boundedness of the local resolvent function. Integral Equations Oper. Theory 34 (1999), 1-8. | DOI | MR | JFM

[6] Bračič, J., Müller, V.: On bounded local resolvents. Integral Equations Oper. Theory 55 (2006), 477-486. | DOI | MR | JFM

[7] Du, H., Jin, P.: Perturbation of spectrums of $2\times 2$ operator matrices. Proc. Am. Math. Soc. 121 (1994), 761-766. | DOI | MR | JFM

[8] Elbjaoui, H., Zerouali, E. H.: Local spectral theory for $2\times2$ operator matrices. Int. J. Math. Math. Sci. 2003 (2003), 2667-2672. | DOI | MR | JFM

[9] Eschmeier, J., Prunaru, B.: Invariant subspaces and localizable spectrum. Integral Equations Oper. Theory 42 (2002), 461-471. | DOI | MR | JFM

[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. | MR | JFM

[11] Han, J. K., Lee, H. Y., Lee, W. Y.: Invertible completions of $2\times 2$ upper triangular operator matrices. Proc. Am. Math. Soc. 128 (2000), 119-123. | DOI | MR | JFM

[12] Houimdi, M., Zguitti, H.: Local spectral properties of a square matrix of operators. Acta Math. Vietnam 25 (2000), 137-144 (in French). | MR | JFM

[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) {\it 56} (1998), 15-25. | MR | JFM

[14] Zerouali, E. H., Zguitti, H.: Perturbation of spectra of operator matrices and local spectral theory. J. Math. Anal. Appl. 324 (2006), 992-1005. | DOI | MR | JFM

[15] Zhong, W.: Method of separation of variables and Hamiltonian system. Comput. Struct. Mech. Appl. 8 (1991), 229-240 (in Chinese).

Cité par Sources :