Siegfried Gähler, Aleksander Misiak
1984 Demonstratio Mathematica  
REMARKS ON 2-INNER PRODUCTS Let L be a linear space of dimension greater than 1· A 2-inner product on L ([l], [4]) is a real function (.,·!·) on L*LxL with the following properties: 1. (a,alb)>0, & 0 if and only if a and b are linearly dependent, 2. (a,a|b) = (b,b|a), 3. (a,b|c) = (b,a|c), 4. (aa,blc) *a(a,b|c) for every real α , 5. (a + a' ,blc) * (a,b|c) + (a',b|c)· (L,(.I.)) is called 2-inner product space or 2-pre-Hilbert space. The concepts of 2-inner produot and 2-inner product space are
more » ... product space are 2-dimeneional analogs of the conoepts of inner product and inner produot space. Let (·,·!.) be a 2-inner product on L. From [l], lemma 2, we know that
doi:10.1515/dema-1984-0309 fatcat:p5zlbuq54rb6tnqv37tpxwmvnm