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- W3152051559 abstract "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, Tao (J. Oper. Theory 82(2) (2019) 369–382) extended the result of Popa (On commutators in properly infinite (W^*)-algebras, in: Invariant subspaces and other topics (1982) (Boston, Mass.: Birkhäuser, Basel)) which reads as: for each (0<varepsilon le 1/2), there exist (D,X in {mathcal {B}}({mathcal {H}})) with (Vert [D,X]-1_{{mathcal {B}}({mathcal {H}})}Vert le varepsilon ) such that (Vert DVert Vert XVert =Oleft( log ^5frac{1}{varepsilon }right) ), where ([D,X]:=DX-XD). In this paper, we show that Tao’s 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)." @default.
- W3152051559 created "2021-04-13" @default.
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- W3152051559 date "2022-03-15" @default.
- W3152051559 modified "2023-09-24" @default.
- W3152051559 title "Commutators close to the identity in unital C*-algebras" @default.
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- W3152051559 doi "https://doi.org/10.1007/s12044-022-00663-w" @default.
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