Operator Hilbert-Schmidt dan aplikasinya

RUHAMA, Mustafa A.H, Prof. Dr. Soeparna Darmawijaya

2008 | Tesis | S2 Matematika

Diketahui 1 H dan 2 H dua ruang Hilbert, ( , ) 1 2 B H H merupakan koleksi semua operator (fungsi linear kontinu) dari 1 H ke 2 H . Jika 1 H separabel dengan basis orthonormal {e n N} n : Î maka ( , ) 1 2 T Î B H H disebut operator Hilbert-Schmidt jika ¥ < Σ ¥ n=1 n Te . Selanjutnya ( , ) 2 1 2 B H H merupakan koleksi semua operator Hilbert-Schmidt. Akan diselidiki sifat-sifat operator Hilbert-Schmidt dan aplikasinya.

Let 1 H and 2 H be two Hilbert spaces and ( , ) 1 2 B H H the collection of operators (continuously linear function) from 1 H into 2 H . If 1 H is separable with {e n N} n : Î is an orthonormal basis of 1 H , ( , ) 1 2 T Î B H H is called an Hilbert-Schmidt operator if ¥ < Σ ¥ n=1 n Te . Furthermore ( , ) 2 1 2 B H H be the collection of Hilbert-Schmidt operators. In this thesis we are going to study properties of Hilbert-Schmidt operators and their applications

Kata Kunci : Hilbert,Schmidt,Fungsi linear kontinue