Fréchet differential of a power series in Banach algebras
We present two new forms in which the Fréchet differential of a power series in a unitary Banach algebra can be expressed in terms of absolutely convergent series involving the commutant \(C(T) : A \mapsto [A,T]\). Then we apply the results to study series of vector-valued functions on domains in Ba...
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| Format: | Article |
| Language: | English |
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AGH Univeristy of Science and Technology Press
2010-01-01
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| Series: | Opuscula Mathematica |
| Subjects: | |
| Online Access: | http://www.opuscula.agh.edu.pl/vol30/2/art/opuscula_math_3011.pdf |
| _version_ | 1819262564762124288 |
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| author | Benedetto Silvestri |
| author_facet | Benedetto Silvestri |
| author_sort | Benedetto Silvestri |
| collection | DOAJ |
| description | We present two new forms in which the Fréchet differential of a power series in a unitary Banach algebra can be expressed in terms of absolutely convergent series involving the commutant \(C(T) : A \mapsto [A,T]\). Then we apply the results to study series of vector-valued functions on domains in Banach spaces and to the analytic functional calculus in a complex Banach space. |
| first_indexed | 2024-12-23T19:59:42Z |
| format | Article |
| id | doaj.art-fd62791f752944b4a6c4f7d3a9b7be5a |
| institution | Directory Open Access Journal |
| issn | 1232-9274 |
| language | English |
| last_indexed | 2024-12-23T19:59:42Z |
| publishDate | 2010-01-01 |
| publisher | AGH Univeristy of Science and Technology Press |
| record_format | Article |
| series | Opuscula Mathematica |
| spelling | doaj.art-fd62791f752944b4a6c4f7d3a9b7be5a2022-12-21T17:33:08ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742010-01-01302155177http://dx.doi.org/10.7494/OpMath.2010.30.2.1553011Fréchet differential of a power series in Banach algebrasBenedetto Silvestri0Dipartimento di Matematica, Pura ed Applicata via Trieste, 63, 35121 Padova, ItalyWe present two new forms in which the Fréchet differential of a power series in a unitary Banach algebra can be expressed in terms of absolutely convergent series involving the commutant \(C(T) : A \mapsto [A,T]\). Then we apply the results to study series of vector-valued functions on domains in Banach spaces and to the analytic functional calculus in a complex Banach space.http://www.opuscula.agh.edu.pl/vol30/2/art/opuscula_math_3011.pdfFréchet differentiation in Banach algebrasfunctional calculus |
| spellingShingle | Benedetto Silvestri Fréchet differential of a power series in Banach algebras Opuscula Mathematica Fréchet differentiation in Banach algebras functional calculus |
| title | Fréchet differential of a power series in Banach algebras |
| title_full | Fréchet differential of a power series in Banach algebras |
| title_fullStr | Fréchet differential of a power series in Banach algebras |
| title_full_unstemmed | Fréchet differential of a power series in Banach algebras |
| title_short | Fréchet differential of a power series in Banach algebras |
| title_sort | frechet differential of a power series in banach algebras |
| topic | Fréchet differentiation in Banach algebras functional calculus |
| url | http://www.opuscula.agh.edu.pl/vol30/2/art/opuscula_math_3011.pdf |
| work_keys_str_mv | AT benedettosilvestri frechetdifferentialofapowerseriesinbanachalgebras |