A coincidence theorem for symmetric multilinear forms
نویسندگان
چکیده
منابع مشابه
Symmetric multilinear forms and polarization of polynomials
We study a generalization of the classical correspondence between homogeneous quadratic polynomials, quadratic forms, and symmetric/alternating bilinear forms to forms in n variables. The main tool is combinatorial polarization, and the approach is applicable even when n! is not invertible in the underlying field.
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In this paper we obtain some versions of weak compactness James’ theorem, replacing bounded linear functionals by polynomials and symmetric multilinear forms. Mathematics Subject Classification (1991): 46B10, 46B50, 46G25
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The conditions under which, multilinear forms (the symmetric case and the non symmetric case),can be written as a product of linear forms, are considered. Also we generalize a result due to S.Kurepa for 2n-functionals in a group G.
متن کاملMultilinear forms
Proposition 1.1. α1, . . . , αn forms a basis for V ∗ (called the dual basis). In particular, this shows that V and V ∗ are vector spaces of the same dimension. However, there is no natural way to choose an isomorphism between them, unless we pick some additional structure on V (such as a basis or a nondegenerate bilinear form). On the other hand, we can construct an isomorphism ψ from V to (V ...
متن کاملCongruence of Multilinear Forms
Let F : U × · · · × U → K, G : V × · · · × V → K be two n-linear forms with n > 2 on vector spaces U and V over a field K. We say that F and G are symmetrically equivalent if there exist linear bijections φ1, . . . , φn : U → V such that F (u1, . . . , un) = G(φi1u1, . . . , φinun) for all u1, . . . , un ∈ U and each reordering i1, . . . , in of 1, . . . , n. The forms are said to be congruent ...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1988
ISSN: 0022-247X
DOI: 10.1016/0022-247x(88)90393-9