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 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 MSC numbers : Primary 46L05; Secondary 46L55, 19K56, 22D25 Downloads: Full-text PDF