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On the inner and outer norms of sublinear mappings Aragón Artacho, Francisco Javier ; in Set-Valued Analysis (2007), 15(1), 61-65 In this short note we show that the outer norm of a sublinear mapping F, acting between Banach spaces X and Y and with dom F = X, is finite only if F is single-valued. This implies in particular that for ... [more ▼] In this short note we show that the outer norm of a sublinear mapping F, acting between Banach spaces X and Y and with dom F = X, is finite only if F is single-valued. This implies in particular that for a sublinear multivalued mapping the inner and the outer norms cannot be finite simultaneously. [less ▲] Detailed reference viewed: 85 (2 UL)A new and self-contained proof of Borwein's norm duality theorem Aragón Artacho, Francisco Javier in Set-Valued Analysis (2007), 15(3), 307-315 Borwein’s norm duality theorem establishes the equality between the outer (inner) norm of a sublinear mapping and the inner (outer) norm of its adjoint mappings. In this note we provide an extended ... [more ▼] Borwein’s norm duality theorem establishes the equality between the outer (inner) norm of a sublinear mapping and the inner (outer) norm of its adjoint mappings. In this note we provide an extended version of this theorem with a new and self-contained proof relying only on the Hahn-Banach theorem. We also give examples showing that the assumptions of the theorem cannot be relaxed. [less ▲] Detailed reference viewed: 101 (3 UL) |
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