On a Class of Composition Operators on Bergman Space
Let 𝔻={z∈ℂ:|z|<1} be the open unit disk in the complex plane ℂ. Let A2(𝔻) be the space of analytic functions on 𝔻 square integrable with respect to the measure dA(z)=(1/π)dx dy. Given a∈𝔻 and f any measurable function on 𝔻, we define the...
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| Format: | Article |
| Language: | English |
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Wiley
2007-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2007/39819 |
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| _version_ | 1850165842324488192 |
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| author | Namita Das R. P. Lal C. K. Mohapatra |
| author_facet | Namita Das R. P. Lal C. K. Mohapatra |
| author_sort | Namita Das |
| collection | DOAJ |
| description | Let 𝔻={z∈ℂ:|z|<1} be the open unit
disk in the complex plane ℂ. Let A2(𝔻) be the space of analytic functions on 𝔻 square integrable
with respect to the measure dA(z)=(1/π)dx dy. Given a∈𝔻 and f any
measurable function on 𝔻, we define the function
Caf by Caf(z)=f(ϕa(z)), where ϕa∈Aut(𝔻). The map Ca is a composition operator on L2(𝔻,dA) and A2(𝔻) for all a∈𝔻. Let ℒ(A2(𝔻)) be the space of
all bounded linear operators from A2(𝔻) into itself. In this article, we have shown that CaSCa=S for all a∈𝔻 if and only if
∫𝔻S˜(ϕa(z))dA(a)=S˜(z), where S∈ℒ(A2(𝔻)) and S˜ is the Berezin symbol of S. |
| format | Article |
| id | doaj-art-e1efed27a6b8436e9d46f10008ab3411 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-e1efed27a6b8436e9d46f10008ab34112025-08-20T02:21:38ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252007-01-01200710.1155/2007/3981939819On a Class of Composition Operators on Bergman SpaceNamita Das0R. P. Lal1C. K. Mohapatra2P. G. Department of Mathematics, Utkal University, Vani Vihar, Bhubaneswar, Orissa 751004, IndiaInstitute of Mathematics and Applications, 2nd Floor, Surya Kiran Building, Sahid Nagar, Bhubaneswar, Orissa 751007, IndiaInstitute of Mathematics and Applications, 2nd Floor, Surya Kiran Building, Sahid Nagar, Bhubaneswar, Orissa 751007, IndiaLet 𝔻={z∈ℂ:|z|<1} be the open unit disk in the complex plane ℂ. Let A2(𝔻) be the space of analytic functions on 𝔻 square integrable with respect to the measure dA(z)=(1/π)dx dy. Given a∈𝔻 and f any measurable function on 𝔻, we define the function Caf by Caf(z)=f(ϕa(z)), where ϕa∈Aut(𝔻). The map Ca is a composition operator on L2(𝔻,dA) and A2(𝔻) for all a∈𝔻. Let ℒ(A2(𝔻)) be the space of all bounded linear operators from A2(𝔻) into itself. In this article, we have shown that CaSCa=S for all a∈𝔻 if and only if ∫𝔻S˜(ϕa(z))dA(a)=S˜(z), where S∈ℒ(A2(𝔻)) and S˜ is the Berezin symbol of S.http://dx.doi.org/10.1155/2007/39819 |
| spellingShingle | Namita Das R. P. Lal C. K. Mohapatra On a Class of Composition Operators on Bergman Space International Journal of Mathematics and Mathematical Sciences |
| title | On a Class of Composition Operators on Bergman Space |
| title_full | On a Class of Composition Operators on Bergman Space |
| title_fullStr | On a Class of Composition Operators on Bergman Space |
| title_full_unstemmed | On a Class of Composition Operators on Bergman Space |
| title_short | On a Class of Composition Operators on Bergman Space |
| title_sort | on a class of composition operators on bergman space |
| url | http://dx.doi.org/10.1155/2007/39819 |
| work_keys_str_mv | AT namitadas onaclassofcompositionoperatorsonbergmanspace AT rplal onaclassofcompositionoperatorsonbergmanspace AT ckmohapatra onaclassofcompositionoperatorsonbergmanspace |