On the Stable Rank of Algebras of Operator Fields over Metric Spaces
نویسندگان
چکیده
Let Γ be a finitely generated, torsion-free, two step nilpotent group. Let C(Γ) be the universal C∗-algebra of Γ. We show that acsr(C∗(Γ)) = acsr(C((Γ̂)1), where for a unital C∗-algebra A, acsr(A) is the absolute connected stable rank of A, and where (Γ̂)1 is the space of one-dimensional representations of Γ. For the case of stable rank, we have close results. In the process, we give a stable rank estimate for maximal full algebras of operator fields over metric spaces.
منابع مشابه
Weighted Composition Operators Between Extended Lipschitz Algebras on Compact Metric Spaces
In this paper, we provide a complete description of weighted composition operators between extended Lipschitz algebras on compact metric spaces. We give necessary and sufficient conditions for the injectivity and the sujectivity of these operators. We also obtain some sufficient conditions and some necessary conditions for a weighted composition operator between these spaces to be compact.
متن کاملFixed point theorems for generalized quasi-contractions in cone $b$-metric spaces over Banach algebras without the assumption of normality with applications
In this paper, we introduce the concept of generalized quasi-contractions in the setting of cone $b$-metric spaces over Banach algebras. By omitting the assumption of normality we establish common fixed point theorems for the generalized quasi-contractions with the spectral radius $r(lambda)$ of the quasi-contractive constant vector $lambda$ satisfying $r(lambda)in [0,frac{1}{s})$ in the set...
متن کاملWeighted composition operators between Lipschitz algebras of complex-valued bounded functions
In this paper, we study weighted composition operators between Lipschitz algebras of complex-valued bounded functions on metric spaces, not necessarily compact. We give necessary and sufficient conditions for the injectivity and the surjectivity of these operators. We also obtain sufficient and necessary conditions for a weighted composition operator between these spaces to be compact.
متن کاملQuasicompact and Riesz unital endomorphisms of real Lipschitz algebras of complex-valued functions
We first show that a bounded linear operator $ T $ on a real Banach space $ E $ is quasicompact (Riesz, respectively) if and only if $T': E_{mathbb{C}}longrightarrow E_{mathbb{C}}$ is quasicompact (Riesz, respectively), where the complex Banach space $E_{mathbb{C}}$ is a suitable complexification of $E$ and $T'$ is the complex linear operator on $E_{mathbb{C}}$ associated with $T$. Next, we pr...
متن کاملOn the Stable Rank of Algebras of Operator Fields over an N-cube
Let A be a unital maximal full algebra of operator fields with base space [0, 1] and fibre algebras {At}t∈[0,1]k . We show that the stable rank of A is bounded above by the quantity supt∈[0,1]ksr(C([0, 1] )⊗ At). Here the symbol “sr” means stable rank. Using the above estimate, we compute the stable ranks of the C-algebras of the (possibly higher rank) discrete Heisenberg groups.
متن کامل