Stable Perturbations of Operators and related topics

Author(s): 
Yifeng Xue
Publisher: 
Word Scientific
Year: 
2012
ISBN: 
13 978-981-4383-59-2
Short description: 

The book studies different analysis perturbation of operators , including Moore-Penrose inverse, and Drazin inverse of operaors .Several miscellaneous applications are also included.

MSC main category: 
46 Functional analysis
Review: 

This book concerns with the theory of stable perturbations of operators in
Banach spaces . Thus the perturbation analysis for generalized inverses, the
Moore-Penrose inverse and Drazin inverse of operators under stable pertur-
bation. After a preliminary chapter including several basic results in Func-
tional Analysis ( Hilbert spaces, operators and C + algebras ) the book studies
carefully the relationships among the densely-defined operators with closed
range and the reduced minimum modulus of densely defined operators . The
Moore-Penrose inverse and its stable perturbations in Hilbert spaces and in
C ∗ -algebras is also presented . Several results of the K-theory in C + algebras
are also included. The last chapters of the book contain some miscellaneous
applications and related topics to the perturbation theory, like the approxi-
mate polar decomposition in C ∗ -algebras, and some applications of Moore-
Penrose inverses in frame theory.The list of references in the Bibliography is
quite extensive.

Reviewer: 
Francisco L. Hernandez
Affiliation: 
Universidad complutense de Madrid

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