Muslim, Ansori (2007) Beberapa Sifat Operator HilbertSchmidt Pada Ruang L2 ( M ). Seminar Nasional Penelitian, Pendidikan dan Penerapan MIPA 2007. ISSN 9789799931429

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Abstract
Let M 1 ⊂ Rm and M 2 ⊂ Rn be measurable sets, respectively. A continuous linear operator K : L 2 ( M1 ) → L2 ( M 2 ) is a HilbertSchmidt operator if and only if there is a function k ∈ L 2 ( M 2 × M 1 ) such that ( Kf )( x ) = ∫ M1 k ( x, y ) f ( y ) dy almost everywhere for every f ∈ L 2 ( M 2 ) ; the function k is called kernel of K . If K is the norm of K , then K = ( ∫ M 2 ∫ M1 k ( x , y ) 2 dydx ) 1 2 = k The collection of the HilbertSchmidt operator from L 2 ( M 1 ) into L 2 ( M 2 ) is denoted by Further, we shal show that K ( M , M ) , M ⊂ Rn , is ∗ algebra in L c ( M , M ) . Keywords : involution, adjoint, ∗ algebra
Item Type:  Article 

Uncontrolled Keywords:  involution, adjoint, ∗ algebra 
Subjects:  Prosiding > Seminar Nasional Penelitian, Pendidikan dan Penerapan MIPA 2007 
Divisions:  Fakultas Matematika dan Ilmu Pengetahuan Alam > Jurusan Pendidikan Matematika 
Depositing User:  Eprints 
Date Deposited:  13 Feb 2015 07:11 
Last Modified:  13 Feb 2015 07:11 
URI:  http://eprints.uny.ac.id/id/eprint/12074 
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