SIFAT S-TIPIKAL OPERATOR PADA RUANG HILBERT; ( S-TYPICAL PROPERTIES OF OPERATOR ON HILBERT SPACES )

Yulianti Rusdiana, Ch. Rini Indrati

2014 | Disertasi | PROGRAM STUDI S2 MATEMATIKA

Let H be an infinite dimensional separable Hilbert space. In this thesis, the set of all contraction operators on H, denoted Ct(H), as a Baire space is proved by showing that Ct(H) is a completely metrizable separable topological space. It means, there exist a metric ds on Ct(H) such that (Ct(H); ds) is a complete separable metric space and the strong topology on Ct(H) is generated by metric ds. Furthemore, a property ? on the point of Baire space Ct(H) is called a typical property on Ct(H) if the set fA 2 Ct(H) : A satisfies ?g is co-meager in Ct(H). The s-typical property on Ct(H) is unitarily equivalent to an infinite-dimensional backward unilateral shift operator. To prove it, we must show that if S is backward unilateral shift operator, then the set O(S) = fUSU

Kata Kunci : SIFAT S-TIPIKAL; OPERATOR; RUANG HILBERT