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- W2080247209 abstract "Let D be the open unit disk in C, and Lh2 the space of quadratic integrable harmonic functions defined on D. Let (varphi : bar D to C) be a function in L∞(D) with the property that ϕ(b) = limx→b,x∈D ϕ(x) for all b ∈ ∂D. Define the operator Cϕ on Lh2 as follows: Cϕ(f) = Q(ϕ · f), where Q is the orthogonal projection of L2(D) onto Lh2. In this paper it is shown that if Cϕ is Fredholm, then ϕ is bounded away from zero on a neighborhood of ∂D. Also, if Cϕ is compact, then ϕ|∂D ≡ 0, and the commutator ideal of τ(D) is K(D), where τ(D) denotes the norm closed subalgebra of the algebra of all bounded operators on Lh2 generated by ({ C_varphi : psi subset C(overline D )} ), and K(D) is the ideal of compact operators on Lh2. Finally, the spectrum of classes of operators defined on Lh2 is characterized." @default.
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- W2080247209 date "1990-05-01" @default.
- W2080247209 modified "2023-09-27" @default.
- W2080247209 title "A Class of Operators on Lh 2" @default.
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- W2080247209 doi "https://doi.org/10.1007/bf03322460" @default.
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