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1999•Proceedings of the American Mathematical SocietyOpen access

Some remarks on the real rank of non-unital C*-algebras

Takashi Sakamoto

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Abstract

For a non-unital C$^{*}$-algebra $A$, let $A^{\sim }$ be the C$^{*}$-algebra obtained from $A$ by adjoining an identity. In this paper we show that \[ \mathrm {RR}( C_{0}(X) \otimes A)=\mathrm {RR} ( C_{0}(X) \otimes A^{\sim }) ,\] where $X$ is a locally compact Hausdorff space with $\mathrm {RR}( C_{0}(X) ) \le 1$.

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For a non-unital C$^{*}$-algebra $A$, let $A^{\sim }$ be the C$^{*}$-algebra obtained from $A$ by adjoining an identity. In this paper we show that \[ \mathrm {RR}( C_{0}(X) \otimes A)=\mathrm {RR} ( C_{0}(X) \otimes A^{\sim }) ,\] where $X$ is a locally compact Hausdorff space with $\mathrm {RR}( C_{0}(X) ) \le 1$.

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Available abstract

For a non-unital C$^{*}$-algebra $A$, let $A^{\sim }$ be the C$^{*}$-algebra obtained from $A$ by adjoining an identity. In this paper we show that \[ \mathrm {RR}( C_{0}(X) \otimes A)=\mathrm {RR} ( C_{0}(X) \otimes A^{\sim }) ,\] where $X$ is a locally compact Hausdorff space with $\mathrm {RR}( C_{0}(X) ) \le 1$.

Key concepts: Unital, Hausdorff space, Mathematics, Rank (graph theory), Identity (music), Space (punctuation), Combinatorics, Pure mathematics

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