scholarly journals An operator representation for weighted inductive limits of spaces of vector valued holomorphic functions

2001 ◽  
Vol 8 (4) ◽  
pp. 577-589 ◽  
Author(s):  
Klaus D. Bierstedt ◽  
Silke Holtmanns
Keyword(s):  
Holomorphic Functions ◽  
Inductive Limits ◽  
Operator Representation ◽  
Weighted Inductive Limits ◽  
Vector Valued

scholarly journals PROJECTIVE DESCRIPTION OF WEIGHTED (LF)-SPACES OF HOLOMORPHIC FUNCTIONS ON THE DISC

2003 ◽  
Vol 46 (2) ◽  
pp. 435-450 ◽  
Author(s):  
Klaus D. Bierstedt ◽  
José Bonet
Keyword(s):  
Double Sequence ◽  
Holomorphic Functions ◽  
Growth Conditions ◽  
Inductive Limits ◽  
Primary 46E10 ◽  
Secondary 30H05 ◽  
Spaces Of Holomorphic Functions ◽  
Weighted Inductive Limits ◽  
Projective Description ◽  
Necessary And Sufficient

AbstractThe topology of certain weighted inductive limits of Fréchet spaces of holomorphic functions on the unit disc can be described by means of weighted sup-seminorms in case the weights are radial and satisfy certain natural assumptions due to Lusky; in the sense of Shields and Williams the weights have to be normal. It turns out that no assumption on the (double) sequence of normal weights is necessary for the topological projective description in the case of o-growth conditions. For O-growth conditions, we give a necessary and sufficient condition (in terms of associated weights) for projective description in the case of (LB)-spaces and normal weights. This last result is related to a theorem of Mattila, Saksman and Taskinen.AMS 2000 Mathematics subject classification: Primary 46E10. Secondary 30H05; 46A13; 46M40

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