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Let $mathcal{H}$ be an infinite dimensional Hilbert space and $mathcal{B}(mathcal{H})$ be the C*-algebra of all bounded linear operators on $mathcal{H}$, equipped with the operator-norm. By improving the Brown-Pearcy construction, Terence Tao in 2018, extended the result of Popa [1981] which reads as : For each $0<varepsilonleq 1/2$, there exist $D,X in mathcal{B}(mathcal{H})$ with $|[D,X]-1_{mathcal{B}(mathcal{H})}|leq varepsilon$ such that $|D||X|=Oleft(log^5frac{1}{varepsilon}right)$, where $[D,X]:= DX-XD$. In this paper, we show that Taos result still holds for certain class of unital C*-algebras which include $mathcal{B}(mathcal{H})$ as well as the Cuntz algebra $mathcal{O}_2$.
We consider a family of dynamical systems (A,alpha,L) in which alpha is an endomorphism of a C*-algebra A and L is a transfer operator for alpha. We extend Exels construction of a crossed product to cover non-unital algebras A, and show that the C*-a
We investigate the notion of tracial $mathcal Z$-stability beyond unital C*-algebras, and we prove that this notion is equivalent to $mathcal Z$-stability in the class of separable simple nuclear C*-algebras.
We answer a question of Takesaki by showing that the following can be derived from the thesis of N-T Shen: If A and B are sigma-unital hereditary C*-subalgebras of C such that ||p - q|| < 1, where p and q are the corresponding open projections, then
Let $A$ be a simple separable unital locally approximately subhomogeneous C*-algebra (locally ASH algebra). It is shown that $Aotimes Q$ can be tracially approximated by unital Elliott-Thomsen algebras with trivial $textrm{K}_1$-group, where $Q$ is t
In this work we characterise the C*-algebras A generated by projections with the property that every pair of projections in A has positive angle, as certain extensions of abelian algebras by algebras of compact operators. We show that this property i