Multiplication and composition operators on the space of formal power series

Boundedness of ⋄ -substitution operator u ⋄ C φ on ℓ p ( β ) , with a weighted Cauchy product ⋄ , is investigated by an inductive argument on the pair ( u , φ ) . As a consequence we get that ℓ p ( β ) is a Banach algebra with respect to weighted Cauchy product. Finally we give some necessary and su...

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Bibliographic Details
Published in:Rendiconti del Circolo matematico di Palermo 2021-08, Vol.70 (2), p.641-651
Main Authors: Estaremi, Y., Jabbarzadeh, M. R.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Banach spaces
Geometry
Mathematical analysis
Mathematics
Mathematics and Statistics
Multiplication
Operators (mathematics)
Power series
Vectors (mathematics)
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Summary:Boundedness of ⋄ -substitution operator u ⋄ C φ on ℓ p ( β ) , with a weighted Cauchy product ⋄ , is investigated by an inductive argument on the pair ( u , φ ) . As a consequence we get that ℓ p ( β ) is a Banach algebra with respect to weighted Cauchy product. Finally we give some necessary and sufficient conditions for compactnss, invertibility and cyclic vectors of multiplication operator M ⋄ , u on ℓ p ( β ) .
ISSN:0009-725X
1973-4409
DOI:10.1007/s12215-020-00512-7