zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
Continuous spectrum, point spectrum and residual spectrum of operator matrices. (English) Zbl 1197.47013
Let $M_C$ denote a $2\times 2$ upper triangular operator matrix of the form $M_C=\left(\smallmatrix A&C\\0&B\endsmallmatrix\right)$, which is acting on the sum of Banach spaces $X\oplus Y$ or Hilbert spaces $H\oplus K$. The authors of this paper characterize the sets $\bigcap_{C\in B(Y,X)} \sigma_c(M_C)$, $\bigcap_{C\in B(K,H)} \sigma_p(M_C)$ and $\bigcap_{C\in B(K,H)} \sigma_r(M_C)$, where $\sigma_c(\cdot)$, $\sigma_p(\cdot)$ and $\sigma_r(\cdot)$ denote the continuous spectrum, the point spectrum and the residual spectrum, respectively.

47A10Spectrum and resolvent of linear operators
Full Text: DOI
[1] 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
[2] Chen, X. L.; Zhang, S. F.; Zhong, H. J.: On the filling in holes problem of operator matrices, Linear algebra appl. 430, 558-563 (2009) · Zbl 1151.47005 · doi:10.1016/j.laa.2008.08.022
[3] Djordjević, D. S.: Perturbations of spectra of operator matrices, J. operator theory 48, 467-486 (2002) · Zbl 1019.47003
[4] Du, H. K.; Pan, J.: Perturbation of spectrums of $2\times 2$ operator matrices, Proc. amer. Math. soc. 121, 761-766 (1994) · Zbl 0814.47016 · doi:10.2307/2160273
[5] Han, J. K.; Lee, H. Y.; Lee, W. Y.: Invertible completions of $2\times 2$ upper triangular operator matrices, Proc. amer. Math. soc. 128, 119-123 (1999) · Zbl 0944.47004 · doi:10.1090/S0002-9939-99-04965-5
[6] Hou, G. L.; Alatancang: Perturbation of spectrums of upper triangular operator matrices, J. systems sci. Math. sci. 26, 257-263 (2006) · Zbl 1208.47009
[7] Hwang, I. S.; Lee, W. Y.: The boundedness below of $2\times 2$ upper triangular operator matrices, Integral equations operator theory 39, 267-276 (2001) · Zbl 0986.47004 · doi:10.1007/BF01332656
[8] Ji, Y. Q.: Quasitriangular+small compact=strongly irreducible, Trans. amer. Math. soc. 351, 4657-4673 (1999) · Zbl 0931.47018
[9] Lee, W. Y.: Weyl’s theorem for operator matrices, Integral equations operator theory 32, 319-331 (1998) · Zbl 0923.47001 · doi:10.1007/BF01203773
[10] Lee, W. Y.: Weyl spectra of operator matrices, Proc. amer. Math. soc. 129, 131-138 (2000) · Zbl 0965.47011
[11] Zhang, S. F.; Zhong, H. J.; Jiang, Q. F.: 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