K₁ of the Compact Operators is Zero

Authors

L. G. Brown
Claude Schochet, Wayne State UniversityFollow

Document Type

Article

Abstract

We prove that K₁ of the compact operators is zero. This theorem has the following operator-theoretic formulation: any invertible operator of the form (identity) + (compact) is the product of (at most eight) multiplicative commutators (A_jB_jA_j⁻¹B_j⁻¹)^±1, where each B_j is of the form (identity) + (compact). The proof uses results of L. G. Brown, R. G. Douglas, and P. A. Fillmore on essentially normal operators and a theorem of A. Brown and C. Pearcy on multiplicative commutators.

Disciplines

Algebra

Comments

First published in the Proceedings of the American Mathematical Society 59(1) (1976, http://dx.doi.org/10.1090/S0002-9939-1976-0412863-0 ), published by the American Mathematical Society.

Recommended Citation

L.G. Brown and C. Schochet, K₁ of the compact operators is zero, Proceedings of the American Mathematical Society 59(1) (1976), 119-122.