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)
Generalized invertibility of operator matrices. (English) Zbl 1264.47001
Let $Z$ be a Banach space, such that $Z=X\oplus Y$ for some closed and complementary subspaces $X$ and $Y$. Then each operator $M\in \Bbb B(Z)$ which is invariant on $X$, has a decomposition into some operators $A\in\Bbb B(X)$, $B\in\Bbb B(Y)$ and $C\in\Bbb B(Y, X)$. In this paper, the authors discuss under which conditions on $A$ and $B$, there exists some $C$ such that $M$ has a generalized inverse, or is left Browder (that is, left Fredholm with finite ascent), or has some other similar properties.

47A05General theory of linear operators
47A10Spectrum and resolvent of linear operators
47A53(Semi-) Fredholm operators; index theories
Full Text: DOI
[1] Cao, X., Browder essential approximate point spectra and hypercyclicity for operator matrices, Linear Algebra Appl. 426 (2007), 317--324. · Zbl 1133.47004 · doi:10.1016/j.laa.2007.05.003
[2] Djordjević, D. S., Perturbations of spectra of operator matrices, J. Operator Theory 48 (2002), 467--486. · Zbl 1019.47003
[3] Hai, G. and Chen, A., Perturbations of right and left spectra for operator matrices, to appear in J. Operator Theory. · Zbl 1261.47010
[4] Han, J. K., Lee, H. Y. and Lee, W. Y., Invertible completions of 2{$\times$}2 upper triangular operator matrices, Proc. Amer. Math. Soc. 128 (2000), 119--123. · Zbl 0944.47004 · doi:10.1090/S0002-9939-99-04965-5
[5] Han, Y. M. and Djordjević, S. V., a-Weyl’s theorem for operator matrices, Proc. Amer. Math. Soc. 130 (2001), 715--722. · Zbl 0994.47013 · doi:10.1090/S0002-9939-01-06110-X
[6] Kolundžija, M. Z., Right invertibility of operator matrices, Funct. Anal. Approx. Comput. 2 (2010), 1--5.
[7] Lee, W. Y., Weyl’s theorem for operator matrices, Integral Equations Operator Theory 32 (1998), 319--331. · Zbl 0923.47001 · doi:10.1007/BF01203773
[8] Zhang, S., Wu, Z. and Zhong, H., Continuous spectrum, point spectrum and residual spectrum of operator matrices, Linear Algebra Appl. 433 (2010), 653--661. · Zbl 1197.47013 · doi:10.1016/j.laa.2010.03.036