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- W1966231767 abstract "Let A be a closed linear operator on a Banach space X. This paper is concerned with the solvability and approximate solutions of the equation Ax=y for a given y^X, especially when X is a Lebesgue space Lp, l^p<°°. The domain, null space, and range will be denoted by D(A N(A), and R(A), respectively. Let {Aa} and {Ba} be two nets, indexed by a directed set JL of bounded linear operators on X with the following properties : (a) Aa^M for all a^Jl] (b) R(Ba}c:D(A) and BaAdABa=I-Aa for all a^Jl; (c) R(Aa)aD(A) for all a^Jl, w-imaAAax=Q for all x^X, and slimaAaAx=Q for all x<=D(A). (d) B*x*=$(a)x* for all x*e=R(A)*(=N(A*) in case D(A)=X) with" @default.
- W1966231767 created "2016-06-24" @default.
- W1966231767 creator A5039575217 @default.
- W1966231767 date "1990-01-01" @default.
- W1966231767 modified "2023-09-25" @default.
- W1966231767 title "Solvability of linear functional equations in Lebesgue spaces" @default.
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- W1966231767 doi "https://doi.org/10.2977/prims/1195170854" @default.
- W1966231767 hasPublicationYear "1990" @default.
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