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The Drazin and Moore-Penrose inverse in $$C^*$$-algebras. (English) Zbl 0943.46031
Summary: We give an explicit representation of the Moore-Penrose inverse in a $$C^*$$-algebra in terms of the Drazin inverse of a quasipolar element, and derive properties of the Moore-Penrose inverse from the theory of the Drazin inverse. Results include an alternative proof that regularity implies Moore-Penrose invertibility, and a simplified proof of the continuity theorem for the Moore-Penrose inverse.

##### MSC:
 46L05 General theory of $$C^*$$-algebras 47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
##### Keywords:
Moore-Penrose inverse; Drazin inverse; quasipolar element