zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
On the filling in holes problem for operator matrices. (English) Zbl 1151.47005
Summary: We consider upper-triangular 2-by-2 operator matrices and are interested in the set that has to be added to certain spectra of the matrix in order to get the union of the corresponding spectra of the two diagonal operators. We show that, in the cases of the Browder essential approximate point spectrum, the upper semi-Fredholm spectrum, or the lower semi-Fredholm spectrum the set in question need not to be an open set but may be just a singleton. In addition, we modify and extend known results on Hilbert space operators to operators on Banach spaces.
MSC:
47A10Spectrum and resolvent of linear operators
47A53(Semi-)Fredholm operators; index theories
47A55Perturbation theory of linear operators
References:
[1]Cao, X. H.; Guo, M. Z.; Meng, B.: Weyl’s theorem for upper triangular operator matrices, Linear algebra appl. 402, 61-73 (2005) · Zbl 1129.47301 · doi:10.1016/j.laa.2004.12.005
[2]Cao, X. H.; Guo, M. Z.; Meng, B.: Semi-Fredholm spectrum and Weyl’s theory for operator matrices, Acta math. Sin. 22, 169-178 (2006) · Zbl 1129.47014 · doi:10.1007/s10114-004-0505-1
[3]Cao, X. H.; Guo, M. Z.; Meng, B.: Drazin spectrum and Weyl’s theorem for operator matrices, J. math. Res. exposition 26, 413-422 (2006) · Zbl 1118.47004
[4]Cao, X. H.: Browder spectra for upper triangular operator matrices, J. math. Anal. appl. 342, 477-484 (2008) · Zbl 1139.47006 · doi:10.1016/j.jmaa.2007.11.059
[5]Djordjević, D. S.: Perturbations of spectra of operator matrices, J. operator theory 48, 467-486 (2002) · Zbl 1019.47003
[6]Djordjević, S. V.; Han, Y. M.: A note on Weyl’s theorem for operator matrices, Proc. amer. Math. soc. 131, 2543-2547 (2002) · Zbl 1041.47006 · doi:10.1090/S0002-9939-02-06808-9
[7]Djordjević, S. V.; Han, Y. M.: Browder’s theorem and spectral continuity, Glasgow math. J. 42, 479-486 (2000) · Zbl 0979.47004 · doi:10.1017/S0017089500030147
[8]Du, H. K.; Pan, J.: Perturbation of spectrums of 2×2 operator matrices, Proc. amer. Math. soc. 121, 761-766 (1994) · Zbl 0814.47016 · doi:10.2307/2160273
[9]Han, J. K.; Lee, H. Y.; Lee, W. Y.: Invertible completions of 2×2 upper triangular operator matrices, Proc. amer. Math. soc. 128, 119-123 (1999) · Zbl 0944.47004 · doi:10.1090/S0002-9939-99-04965-5
[10]Hwang, I. S.; Lee, W. Y.: The boundedness below of 2×2 upper triangular operator matrices, Integral equations operator theory 39, 267-276 (2001) · Zbl 0986.47004 · doi:10.1007/BF01332656
[11]Lee, W. Y.: Weyl’s theorem for operator matrices, Integral equations operator theory 32, 319-331 (1998) · Zbl 0923.47001 · doi:10.1007/BF01203773
[12]Lee, W. Y.: Weyl spectra of operator matrices, Proc. amer. Math. soc. 129, 131-138 (2000)
[13]Zhang, Shifang; Zhong, Huaijie: A note of Browder spectrum of operator matrices, J. math. Anal. appl. 344, 927-931 (2008) · Zbl 1146.47004 · doi:10.1016/j.jmaa.2008.03.048
[14]Zhang, Shifang; Zhong, Huaijie; Jiang, Qiaofen: Drazin spectrum of operator matrices on the Banach space, Linear algebra appl. 429, 2067-2075 (2008) · Zbl 1157.47004 · doi:10.1016/j.laa.2008.06.002
[15]Zhang, Yunnan; Zhong, Huaijie; Lin, Liqiong: Browder spectra and essential spectra of operator matrices, Acta math. Sin. 24, 947-954 (2008) · Zbl 1162.47004 · doi:10.1007/s10114-007-6339-x