Search results for "Multilinear map"
showing 10 items of 35 documents
On the ∗-cocharacter sequence of 3×3 matrices
2000
Abstract Let M 3 (F) be the algebra of 3×3 matrices with involution * over a field F of characteristic zero. We study the ∗ -polynomial identities of M 3 (F) , where ∗=t is the transpose involution, through the representation theory of the hyperoctahedral group B n . After decomposing the space of multilinear ∗ -polynomial identities of degree n under the B n -action, we determine which irreducible B n -modules appear with non-zero multiplicity. In symbols, we write the nth ∗ -cocharacter χ n (M 3 (F),*)=∑ r=0 n ∑ λ⊢r,h(λ)⩽6 μ⊢n−r,h(μ)⩽3 m λ,μ χ λ,μ , where λ and μ are partitions of r and n−r , respectively, χ λ,μ is the irreducible B n -character associated to the pair (λ,μ) and m λ,μ ⩾0 i…
Ordinary and graded cocharacter of the Jordan algebra of 2x2 upper triangular matrices
2014
Abstract Let F be a field of characteristic zero and U J 2 ( F ) be the Jordan algebra of 2 × 2 upper triangular matrices over F . In this paper we give a complete description of the space of multilinear graded and ordinary identities in the language of Young diagrams through the representation theory of a Young subgroup of S n . For every Z 2 -grading of U J 2 ( F ) we compute the multiplicities in the graded cocharacter sequence and furthermore we compute the ordinary cocharacter.
On Composition Ideals of Multilinear Mappings and Homogeneous Polynomials
2007
Given an operator ideal I, we study the multi-ideal I ο L and the polynomial ideal I ο P). The connection with the linearizations of these mappings on projective symmetric tensor products is investigated in detail. Applications to the ideals of strictly singular and absolutely summing linear operators are obtained.
Complemented Subspaces and Interpolation Properties in Spaces of Polynomials
1997
LetXbe a Banach space whose dualX* has typep ∈ (1, 2]. Ifmis an integer greater thanp/(p − 1) and (xn) is a seminormalized sequence weakly convergent to zero, there is a subsequence (yn) of (xn) such that, for each element (an) ofl∞, there is anm-homogeneous continuous polynomialPonXwithP(yn) = an,n = 1, 2,… . Some interpolation and complementation properties are also given in P(mlp), form < p, as well as in other spaces of polynomials and multilinear functionals.
Internal Test Sets Studies in a Group of Antimalarials
2006
Topological indices have been applied to build QSAR models for a set of 20 an- timalarial cyclic peroxy cetals. In order to evalua te the reliability of the proposed linear models leave-n-out and Internal Test Sets (ITS) approaches have b een considered. The pro- posed procedure resulted in a robust and consensued prediction equation and here it is shown why it is superior to the employed standard c ross-validation algorithms involving multilinear regression models.
On minimal ∗-identities of matrices∗
1995
Let Mn (F) be the algebra of n×n matrices (n≥2) over a field F of characteristic different from 2 and let ∗ be an involution in Mn (F) In case ∗ is the transpose involution, we construct a multilinear ∗ polynomial identify of Mn (F) of degree 2n−1, P 2n−1(k 1, s 2, … s 2n−1) in one skew variable and the remaining symmetric variables of minimal degree among all ∗-polynomial identities of this type. We also prove that any other multilinear ∗-polynomial identity of Mn (F) of this type of degree 2n−1 is a scalar multiple of P2n−1 . In case ∗ is the symplectic involution in Mn (F), we construct a ∗-polynomial identity of Mn (F) of degree 2n−1 in skew variables T2n−1 (k 1,…,k 2n−1) and we prove t…
On the size of the set of unbounded multilinear operators between Banach spaces
2020
Among other results we investigate $\left( \alpha,\beta\right) $-lineability of the set of non-continuous $m$-linear operators defined between normed spaces as a subset of the space of all $m$-linear operators. We also give a partial answer to an open problem on the lineability of the set of non absolutely summing operators.
DesMol2, an Effective Tool for the Construction of Molecular Libraries and Its Application to QSAR Using Molecular Topology
2019
A web application, DesMol2, which offers two main functionalities, is presented: the construction of molecular libraries and the calculation of topological indices. These functionalities are explained through a practical example of research of active molecules to the formylpeptide receptor (FPR), a receptor associated with chronic inflammation in systemic amyloidosis and Alzheimer&rsquo
Traced tensor norms and multiple summing multilinear operators
2016
[EN] Using a general tensor norm approach, our aim is to show that some distinguished classes of summing operators can be characterized by means of an 'order reduction' procedure for multiple summing multilinear operators, which becomes the keystone of our arguments and can be considered our main result. We work in a tensor product framework involving traced tensor norms and the representation theorem for maximal operator ideals. Several applications are given not only to multi-ideals, but also to linear operator ideals. In particular, we get applications to multiple p-summing bilinear operators, (p, q)-factorable linear operators, tau(p)-summing linear operators and absolutely p-summing li…
Equivalence of the Pecka–Ponec Correlation Probability and the Statistical F Significance for MLR Models
2004
In an article of this journal Pecka and Ponec [J. Math. Chem. 27 (2000) 13] have proposed, by means of a probability calculation, a method to evaluate the statistical importance of correlations obtained from multilinear regression equations involving an arbitrary number of experimental points and parameters. Here, it is demonstrated how this probability exactly coincides with a more general concept: the confidence probability of an F distribution having the appropriate degrees of freedom.