Displaying similar documents to “Some results in the metric theory of tensor products”

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.

A Spectral Theory for Tensors

Edinah K. Gnang, Ahmed Elgammal, Vladimir Retakh (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

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In this paper we propose a general spectral theory for tensors. Our proposed factorization decomposes a tensor into a product of orthogonal and scaling tensors. At the same time, our factorization yields an expansion of a tensor as a summation of outer products of lower order tensors. Our proposed factorization shows the relationship between the eigen-objects and the generalised characteristic polynomials. Our framework is based on a consistent multilinear algebra which explains how...

Invertibility in tensor products of Q-algebras

Seán Dineen, Pablo Sevilla-Peris (2002)

Studia Mathematica

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We consider, using various tensor norms, the completed tensor product of two unital lmc algebras one of which is commutative. Our main result shows that when the tensor product of two Q-algebras is an lmc algebra, then it is a Q-algebra if and only if pointwise invertibility implies invertibility (as in the Gelfand theory). This is always the case for Fréchet algebras.