Geometry of bilinear forms on the plane with hexagonal norms

초록

Let 0 < w<inf>1</inf>, w<inf>2</inf> < 1. We denote by R2<inf>h(w1,w2)</inf>the plane with the hexagonal norm ∥(x, y)∥<inf>h(w1,w2)</inf>= max { |y|, w<inf>1</inf> |x| + w<inf>2</inf> |y|}. We denote by R2<inf>h′ (w1,w2)</inf> the plane with the hexagonal norm ∥(x, y)∥<inf>h′ (w1,w2)</inf>= max {|x|, w<inf>1</inf> |x| + w<inf>2</inf> |y|}. In this paper, we classify the extreme bilinear forms of the unit balls of L(2X) and L<inf>s</inf>(2X), where X = R2<inf>h(w1,w2)</inf>or R2<inf>h′(w1,w2).</inf> From this, we induce that ext B<inf>Ls</inf>(2X) = ext B<inf>L(</inf>2X) ∩ L<inf>s</inf>(2X). We show that every extreme bilinear forms on that spaces is exposed. © Palestine Polytechnic University-PPU 2024.

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