Open AccessGeometry of bilinear forms on the plane with the octagonal norm
Author(s) -
Sung Guen Kim,
AUTHOR_ID
Publication year - 2021
Publication title -
bulletin of the "transilvania" university of braşov. series iii, mathematics and computer science
Language(s) - English
Resource type - Journals
eISSN - 2810-2037
pISSN - 2810-2029
DOI - 10.31926/but.mif.2021.1.63.1.12
Subject(s) - bilinear interpolation , geometry , mathematics , subspace topology , norm (philosophy) , bilinear form , combinatorics , plane (geometry) , mathematical analysis , statistics , political science , law
LetR2o(w)be the plane with the octagonal norm with weight 0< w,w6= 1‖(x,y)‖o(w)= max{|x|+w|y|,|y|+w|x|}.In this paper we classify all extreme, exposed and smooth points of the closedunit balls ofL(2R2o(w)) andLs(2R2o(w)),whereL(2R2o(w)) is the space of bi-linear forms onR2o(w),andLs(2R2o(w)) is the subspace ofL(2l2∞,θ) consistingof symmetric bilinear forms.