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- W2120577936 abstract "Suppose $T$ is a continuous linear operator between two Hilbert spaces $X$ and $Y$ and let $K$ be a closed convex nonempty cone in $X$. We investigate the possible existence of $delta > 0$ such that $delta B_Y cap T(K) subseteq T(B_X cap K)$, where $B_X,B_Y$ denote the closed unit balls in $X$ and $Y$ respectively. This property, which we call openness relative to $K$, is a generalization of the classical openness of linear operators. We relate relative openness to Jameson's property~(G), to the strong conical hull intersection property, to bounded linear regularity, and to metric regularity. Our results allow a simple construction of two closed convex cones that have the strong conical hull intersection property but fail to be boundedly linearly regular." @default.
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- W2120577936 date "1999-01-01" @default.
- W2120577936 modified "2023-10-18" @default.
- W2120577936 title "Conical open mapping theorems and regularity" @default.
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