# Continuity of generalized inverses in Banach algebras

Steffen Roch; Bernd Silbermann

Studia Mathematica (1999)

- Volume: 136, Issue: 3, page 197-227
- ISSN: 0039-3223

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topRoch, Steffen, and Silbermann, Bernd. "Continuity of generalized inverses in Banach algebras." Studia Mathematica 136.3 (1999): 197-227. <http://eudml.org/doc/216668>.

@article{Roch1999,

abstract = {The main topic of the paper is the continuity of several kinds of generalized inversion of elements in a Banach algebra with identity. We introduce the notion of asymptotic generalized invertibility and completely characterize sequences of elements with this property. Based on this result, we derive continuity criteria which generalize the well known criteria from operator theory.},

author = {Roch, Steffen, Silbermann, Bernd},

journal = {Studia Mathematica},

keywords = {generalized inverses; Drazin inverses; Moore-Penrose inverses; group inverses; symmetric inverses; asymptotic generalized invertibility; problem of continuity of a generalized inverse; regularization; asymptotic splitting of approximation numbers},

language = {eng},

number = {3},

pages = {197-227},

title = {Continuity of generalized inverses in Banach algebras},

url = {http://eudml.org/doc/216668},

volume = {136},

year = {1999},

}

TY - JOUR

AU - Roch, Steffen

AU - Silbermann, Bernd

TI - Continuity of generalized inverses in Banach algebras

JO - Studia Mathematica

PY - 1999

VL - 136

IS - 3

SP - 197

EP - 227

AB - The main topic of the paper is the continuity of several kinds of generalized inversion of elements in a Banach algebra with identity. We introduce the notion of asymptotic generalized invertibility and completely characterize sequences of elements with this property. Based on this result, we derive continuity criteria which generalize the well known criteria from operator theory.

LA - eng

KW - generalized inverses; Drazin inverses; Moore-Penrose inverses; group inverses; symmetric inverses; asymptotic generalized invertibility; problem of continuity of a generalized inverse; regularization; asymptotic splitting of approximation numbers

UR - http://eudml.org/doc/216668

ER -

## References

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- [14] M. Z. Nashed (ed.), Generalized Inverses and Applications, Academic Press, New York, 1976.
- [15] V. Rakočević, Continuity of the Drazin inverse, J. Operator Theory 41 (1999), 55-68. Zbl0990.47002
- [16] S. Roch and B. Silbermann, C*-algebra techniques in numerical analysis, ibid. 35 (1996), 241-280. Zbl0865.65035
- [17] S. Roch and B. Silbermann, Asymptotic Moore-Penrose invertibility of singular integral operators, Integral Equations Operator Theory 26 (1996), 81-101. Zbl0860.65145
- [18] S. Roch and B. Silbermann, Index calculus for approximation methods, and singular value decomposition, J. Math. Anal. Appl. 225 (1998), 401-426. Zbl0923.65026
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