Geodesic
DIRECTLY FINITE ALGEBRAS OF PSEUDOFUNCTIONS ON LOCALLY COMPACT GROUPS
Glasgow mathematical journal, Tome 57 (2015) no. 3, pp. 693-707

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DOI

An algebra A is said to be directly finite if each left-invertible element in the (conditional) unitization of A is right invertible. We show that the reduced group C*-algebra of a unimodular group is directly finite, extending known results for the discrete case. We also investigate the corresponding problem for algebras of p-pseudofunctions, showing that these algebras are directly finite if G is amenable and unimodular, or unimodular with the Kunze–Stein property. An exposition is also given of how existing results from the literature imply that L1(G) is not directly finite when G is the affine group of either the real or complex line. 
CHOI, YEMON. DIRECTLY FINITE ALGEBRAS OF PSEUDOFUNCTIONS ON LOCALLY COMPACT GROUPS. Glasgow mathematical journal, Tome 57 (2015) no. 3, pp. 693-707. doi: 10.1017/S0017089514000573
@article{10_1017_S0017089514000573,
     author = {CHOI, YEMON},
     title = {DIRECTLY {FINITE} {ALGEBRAS} {OF} {PSEUDOFUNCTIONS} {ON} {LOCALLY} {COMPACT} {GROUPS}},
     journal = {Glasgow mathematical journal},
     pages = {693--707},
     year = {2015},
     volume = {57},
     number = {3},
     doi = {10.1017/S0017089514000573},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089514000573/}
}
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