Some algebraic properties of F(X) and K(X)
1975 ◽
Vol 19
(4)
◽
pp. 353-361
◽
Keyword(s):
Throughout we consider operators on a reflexive Banach space X. We consider certain algebraic properties of F(X), K(X) and B(X) with the general aim of examining their dependence on the possession by X of the approximation property. B(X) (resp. K(X)) denotes the algebra of all bounded (resp. compact) operators on X and F(X) denotes the closure in B(X) of its finite rank operators. The two questions we consider are:(1) Is K(X) equal to the set of all operators in B(X) whose right and left multiplication operators on F(X) (or on B(X)) are weakly compact?(2) Is F(X) a dual algebra?
1969 ◽
Vol 1
(3)
◽
pp. 397-401
◽
Keyword(s):
2004 ◽
Vol 77
(1)
◽
pp. 91-110
◽
Keyword(s):
1989 ◽
Vol 39
(3)
◽
pp. 353-359
◽
2013 ◽
Vol 56
(3)
◽
pp. 503-509
◽
1962 ◽
Vol 12
(3)
◽
pp. 1023-1027
◽
1982 ◽
Vol 25
(3)
◽
pp. 339-343
◽
Keyword(s):
2018 ◽
Vol 61
(03)
◽
pp. 545-555
◽
Keyword(s):