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STABLE RANKS OF MULTIPLIER ALGEBRAS OF C*-ALGEBRAS
Sudo, Takahiro Korean Mathematical Society 2002 대한수학회논문집 Vol.17 No.3
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.
K-THEORY OF C*-ALGEBRAS OF LOCALLY TRIVIAL CONTINUOUS FIELDS
SUDO TAKAHIRO Korean Mathematical Society 2005 대한수학회논문집 Vol.20 No.1
It is shown that the K-theory of the $C^{\ast}$-algebras of continuous fields on locally compact Hausdorff spaces with fibers elementary $C^{\ast}$-algebras is the same as the K-theory of the base spaces. We also consider the slightly generalized case. Furthermore, we give some applications of these results.
Crossed Products of the Free Group and Semigroup C -algebras by Flows
Takahiro Sudo 한국수학교육학회 2007 純粹 및 應用數學 Vol.14 No.4
We study crossed products of the free group and semigroup C-algebras by actions of R, i.e., flows, and estimate and compute their stable rank.
REAL RANK OF C¤-ALGEBRAS OF TYPE I
Takahiro SUDO 한국수학교육학회 2010 純粹 및 應用數學 Vol.17 No.4
We estimate the real rank of a composition series of closed ideals of a C*-algebra such that its subquotients have continuous trace, which is equivalent to that the C*-algebra is of type I.
K-theory of Crossed Products of $C^*$-algebras Two Metric Spaces
Takahiro SUDO 한국수학교육학회 2005 純粹 및 應用數學 Vol.12 No.1
We study continuous ¯elds and K-groups of crossed products of C¤- algebras. It is shown under a reasonable assumption that there exist continuous ¯elds of C¤-algebras between crossed products of C¤-algebras by amenable locally compact groups and tensor products of C¤-algebras with their group C¤-algebras, and their K-groups are the same under the additional assumptions.
The Real Rank of CCR C*-Algebra
Sudo, Takahiro Department of Mathematics 2008 Kyungpook mathematical journal Vol.48 No.2
We estimate the real rank of CCR C*-algebras under some assumptions. A applications we determine the real rank of the reduced group C*-algebras of non-compac connected, semi-simple and reductive Lie groups and that of the group C*-algebras of connected nilpotent Lie groups.
Stable Rank of Group C^(*)-algebras of Some Disconnected Lie Groups
SUDO, TAKAHIRO 대한수학회 2007 Kyungpook mathematical journal Vol.47 No.2
We estimate the stable rank and connected stable rank of group C^(*)-algebras of certain disconnected solvable Lie groups such as semi-direct products of connected solvable Lie groups by the integers.