Banach algebras for which left invertible implies invertible

Asked Mar 31 '22 at 12:51

Active Mar 31 '22 at 12:51

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Are there noncommutative Banach algebras in which left invertibility implies invertibility? If so, what are they called?

asked Mar 31 '22 at 12:51

Andre

2

How about matrix algebras? Every Banach algebra with topological stable rank 1 has this property:
M.A. Rieffel, Dimension and stable rank in the K-theory of C*-algebras, Proc. Lond. Math. Soc., III. Ser. 46 (1983), 301–333. (Proposition 3.1).
– Tomasz Kania Mar 31 '22 at 12:58
Thanks Tomasz. Will check and update comment again if it does what I hope it does – Andre Mar 31 '22 at 13:20
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Tomasz avoided autopromotion, but his paper with S. Draga is relevant (+1 to both). – Duchamp Gérard H. E. Mar 31 '22 at 20:26
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Usually the terms Dedekind finite or von Neumann finite are used – Benjamin Steinberg Mar 31 '22 at 20:28

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