Displaying similar documents to “Tensor product in symmetric function spaces.”

On tensor functions whose gradients have some skew-symmetries

Adriano Montanaro (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Let V n be a real inner product space of any dimension; and let Q α 1 ⁢ … ⁢ α v = Q ⌃ α 1 ⁢ … ⁢ α v ⁢ X β ⁢ 1 ⁢ … ⁢ β τ be a C 2 -map relating any two tensor spaces on V n . We study the consequences imposed on the form of this function by the condition that its gradient should be skew-symmetric with respect to some pairs α μ , β η of indexes. Any such a condition is written as a system of linear partial differential equations, with constant coefficients, which is symmetric with respect to certain couples of independent variables. The solutions of these...

On the structure of tensor norms related to (p,σ)-absolutely continuous operators.

Enrique A. Sánchez-Pérez (1996)

Collectanea Mathematica

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We define an interpolation norm on tensor products of p-integrable function spaces and Banach spaces which satisfies intermediate properties between the Bochner norm and the injective norm. We obtain substitutes of the Chevet-Persson-Saphar inequalities for this case. We also use the calculus of traced tensor norms in order to obtain a tensor product description of the tensor norm associated to the interpolated ideal of (p, sigma)-absolutely continuous operators defined by Jarchow and...

New criteria for H-tensors and an application

Feng Wang, Deshu Sun (2015)

Open Mathematics

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Some new criteria for identifying H-tensors are obtained. As an application, some sufficient conditions of the positive definiteness for an even-order real symmetric tensor are given. Advantages of results obtained are illustrated by numerical examples.

The symmetric tensor product of a direct sum of locally convex spaces

José Ansemil, Klaus Floret (1998)

Studia Mathematica

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An explicit representation of the n-fold symmetric tensor product (equipped with a natural topology τ such as the projective, injective or inductive one) of the finite direct sum of locally convex spaces is presented. The formula for ⨂ τ , s n ( F 1 ⨁ F 2 ) gives a direct proof of a recent result of Díaz and Dineen (and generalizes it to other topologies τ) that the n-fold projective symmetric and the n-fold projective “full” tensor product of a locally convex space E are isomorphic if E is isomorphic to...

On the domain of applicability of the Mori-Tanaka effective medium theory

Mauro Ferrari (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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The Mori-Tanaka effective stiffness tensor is shown to be asymmetric in general. This tensor is proven to be symmetric for composites with isotropic inclusions, or with spherical reinforcements. Symmetry is also proven for the case of unidirectional fibers, of any shape and material. The Mori-Tanaka theory is shown to yield physically unacceptable predictions at the high concentration limit.

Copies of l in tensor products.

Fernando Blasco (2000)

Extracta Mathematicae

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The problem of finding complemented copies of l in another space is a classical problem in Functional Analysis and has been studied from different points of view in the literature. Here we pay attention to complementation of l in an n-fold tensor product of l spaces because we were lead to that result in the study of Grothendieck's Problème des topologies as we shall comment later.