Multipliers on Fréchet algebra
This paper is devoted to establish some fundamentally important results on a commutative semi simple Fréchet algebra. It has been shown that a multiplier on a semi simple Fréchet algebra is a product of an idempotent and an invertible multiplier. It has also been shown that a multiplier on a commu...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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IDOSI Publications
2013
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/29962/ http://irep.iium.edu.my/29962/ http://irep.iium.edu.my/29962/1/12.pdf |
| Summary: | This paper is devoted to establish some fundamentally important results on a commutative semi simple Fréchet algebra. It has been shown that a multiplier on a semi simple Fréchet algebra is a product of an idempotent and an invertible multiplier. It has also been shown that a multiplier on a commutative semi simple Fréchet algebra which is also a Fredholm operator is a product of an idempotent and an invertible element of a continuous linear self mapping of commutative semi simple Fréchet algebra. Finally have shown that for a multiplier T on a commutative semi simple Fréchet algebra A, T2(A) is closed iff
T(A) + Ker (T) is closed, T(A) + Ker(T) is closed
iff A=T(A)+Ker(T)and T is a product of an idempotent and
an invertible multiplier iff = T(A)+Ker(T).
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