Boundedness and completeness in locally convex spaces and algerbras
1977 ◽
Vol 24
(1)
◽
pp. 50-63
◽
Keyword(s):
AbstractThe set of bounded elements of a unital l.m.c. algebra is characterised as the union of certain naturally defined normed subalgebras, and an analogous characterisation is given for algebras of quotient-bounded operators on a locally convex space. Pseudocomplete l.m.c. algebras are characterised in terms of the completeness of these subalgebras, and the equivalence of this condition with the pseudocompleteness of the quotient-bounded operator algebras established. The scalar multiples of the identity in a unital l.m.c. algebra are characterised in terms of certain boundedness conditions.
2002 ◽
Vol 15
(2)
◽
pp. 91-103
Keyword(s):
1967 ◽
Vol 15
(4)
◽
pp. 295-296
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Keyword(s):
1980 ◽
Vol 88
(2)
◽
pp. 331-337
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Keyword(s):
1985 ◽
Vol 31
(3)
◽
pp. 451-462
Keyword(s):
1983 ◽
Vol 27
(2)
◽
pp. 269-283
2020 ◽
pp. 2050027
Keyword(s):
2014 ◽
Vol 57
(4)
◽
pp. 803-809
◽
Keyword(s):
2010 ◽
Vol 47
(3)
◽
pp. 299-310
Keyword(s):