Spectral Theory Examples
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چکیده
Example 1 (Spectrum of Multiplication Operators) Let • (X, M, µ) be a σ–finite (actually semifinite will do) measure space, • 1 ≤ p ≤ ∞ and • a : X → C be a bounded measurable function on X. (Aϕ)(x) = a(x)ϕ(x) Point spectrum: Let λ ∈ C. Then λ1l − A is injective ⇐⇒ ϕ ∈ L p (X, M, µ), (λ − a(x))ϕ(x) = 0 a.e. =⇒ ϕ(x) = 0 a.e. ⇐⇒ λ − a(x) = 0 a.e.
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تاریخ انتشار 2014