THE CLOSED RANGE PROPERTY FOR BANACH SPACE OPERATORS
2008 ◽
Vol 50
(1)
◽
pp. 17-26
◽
Keyword(s):
Open Set
◽
AbstractLetTbe a bounded operator on a complex Banach spaceX. LetVbe an open subset of the complex plane. We give a condition sufficient for the mappingf(z)↦ (T−z)f(z) to have closed range in the Fréchet spaceH(V,X) of analyticX-valued functions onV. Moreover, we show that there is a largest open setUfor which the mapf(z)↦ (T−z)f(z) has closed range inH(V,X) for allV⊆U. Finally, we establish analogous results in the setting of the weak–* topology onH(V, X*).
1998 ◽
Vol 40
(3)
◽
pp. 427-430
◽
Keyword(s):
1995 ◽
Vol 118
(2)
◽
pp. 315-320
◽
Keyword(s):
1973 ◽
Vol 25
(3)
◽
pp. 468-474
◽
Keyword(s):
1985 ◽
Vol 97
(2)
◽
pp. 321-324
Keyword(s):
2002 ◽
Vol 73
(1)
◽
pp. 115-126
◽
Keyword(s):
1990 ◽
Vol 32
(3)
◽
pp. 273-276
◽
1970 ◽
Vol 17
(2)
◽
pp. 121-125
◽
Keyword(s):