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)
Splittings of operators and generalized inverses. (English) Zbl 0981.47001
Summary: We extend the notion of the proper splitting of rectangular matrices introduced and investigated in Berman, A. and Neumann, M. [SIAM J. Appl. Math. 31, 307-312 (1976; Zbl 0352.65017)] and Berman, A. and Plemmons, R. J. [SIAM J. Numer. Anal. 11, 145-154 (1974; Zbl 0273.65029)] to g-invertible operators on Banach spaces. Also, we extend and generalize the notion of the index splitting of square matrices introduced and investigated in Wei, Y. [Appl. Math. Comput. 95, 115-124 (1998; Zbl 0942.15003)] introducing the {T,S}-splitting for arbitrary operators on Banach spaces. The index splitting is a partial case of {T,S}-splitting. The obtained results extend and generalize various well-known results for square and rectangular complex matrices.

MSC:
47A05General theory of linear operators
15A09Matrix inversion, generalized inverses
47A50Equations and inequalities involving linear operators, with vector unknowns
65F20Overdetermined systems, pseudoinverses (numerical linear algebra)
65J10Equations with linear operators (numerical methods)