KOMPLEMEN NORMAL DAN OPERATOR-OPERATOR PADA RUANG INNER PRODUK NON-ARCHIMEDEAN c0(K); ( NORMAL COMPLEMENT AND OPERATORS ON NON-ARCHIMEDEAN INNER PRODUCT SPACE c0(K) )

Hasman, Zulijanto, Atok

2015 | Disertasi | FMIPA UGM

In this thesis, we study a closed subspace of the non-Archimedean inner product space (c0(K); h:; :i) which has a normal complement, that is, a closed subspace M ? c0(K) such that c0(K) = M ? M? and hx; yi = 0 for all x 2 M and y 2 M?. Among the subspaces which have normal complement are finitedimensional subspaces, closed subspaces that have an orthonormal basis with the Riemann-Lebesgue property and null spaces of Riez functional. In addition, in this thesis, we also discuss about normal projection, adjoint and self adjoint operators on non-Archimedean inner product space c0(K).

Kata Kunci : INNER PRODUCT SPACE