Beberapa Sifat Operator Hilbert-Schmidt Pada Ruang L2 ( M )

Muslim, Ansori (2007) Beberapa Sifat Operator Hilbert-Schmidt Pada Ruang L2 ( M ). Seminar Nasional Penelitian, Pendidikan dan Penerapan MIPA 2007. ISSN 978-979-99314-2-9

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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 Hilbert-Schmidt 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 Hilbert-Schmidt 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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