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Some remarks on the space of differences of sublinear functions

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Bartels S. G., Pallaschke D.

Applicationes Mathematicae

1993-1995

tom 22

nr 3

419-426

Two properties concerning the space of differences of sublinear functions D(X) for a real Banach space X are proved. First, we show that for a real separable Banach space (X,‖·‖) there exists a countable family of seminorms such that D(X) becomes a Fréchet space. For X = ℝ^n this construction yields a norm such that D(ℝ^n) becomes a Banach space. Furthermore, we show that for a real Banach space with a smooth dual every sublinear Lipschitzian function can be expressed by the Fenchel conjugate of the farthest point mapping to its subdifferential at the origin. This leads to a simple family of sublinear functions which contains an exhaustive family of upper convex approximations for any quasidifferentiable function.

Ograniczanie wyników

1 Applicationes Mathematicae

1 Bartels S. G.

1 Pallaschke D.

1 1994

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Some remarks on the space of differences of sublinear functions