Stable ranks of multiplier algebras of $C^*$-algebras
Commun. Korean Math. Soc. 2002 Vol. 17, No. 3, 475-485 Printed September 1, 2002
Takahiro Sudo University of the Ryukyus
Abstract : We estimate the stable rank, connected stable rank and general stable rank of the multiplier algebras of $C^*$-algebras under some conditions and prove that the ranks of them are infinite. Moreover, we show that for any $\sigma$-unital subhomogeneous $C^*$-algebra, its stable rank is equal to that of its multiplier algebra.
Keywords : stable rank, multiplier, group $C^*$-algebra, subhomogeneous $C^*$-algebra