Geodesic
Complete continuity for a class of Banach algebras
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 29, Tome 282 (2001), pp. 139-159

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For the quotiens of group algebras, the elements are studied that yield a compact (left or right) multiplication operator. The spectrum of such an algebra is analyzed in the case where all such (left or right) multiplication operators are weakly compact. 
@article{ZNSL_2001_282_a10,
     author = {H. S. Mustafaev},
     title = {Complete continuity for a class of {Banach} algebras},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {139--159},
     publisher = {mathdoc},
     volume = {282},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2001_282_a10/}
}
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H. S. Mustafaev. Complete continuity for a class of Banach algebras. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 29, Tome 282 (2001), pp. 139-159. http://geodesic.mathdoc.fr/item/ZNSL_2001_282_a10/