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Locally convex spaces --- Tensor products --- Linear operators --- Nuclear spaces (Functional analysis)

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Tensor products. --- Produits tensoriels. --- Espaces d'operateurs lineaires continus --- Ideaux normes

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Topological groups. Lie groups --- Category theory. Homological algebra --- Homology theory --- Lie groups --- Tensor products --- Homologie --- Groupes de Lie --- Produits tensoriels --- Homology theory. --- Lie groups. --- Tensor products. --- Groupes topologiques --- Topological groups

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The three chapters of this book are entitled Basic Concepts, Tensor Norms, and Special Topics. The first may serve as part of an introductory course in Functional Analysis since it shows the powerful use of the projective and injective tensor norms, as well as the basics of the theory of operator ideals. The second chapter is the main part of the book: it presents the theory of tensor norms as designed by Grothendieck in the Resumé and deals with the relation between tensor norms and operator ideals. The last chapter deals with special questions. Each section is accompanied by a series

Tensor products. --- Operator ideals. --- Ideals (Algebra) --- Products, Tensor --- Algebras, Linear --- Calculus of tensors --- Tensor algebra --- Espaces vectoriels topologiques --- Espaces d'operateurs lineaires continus --- Produits tensoriels --- Ideaux normes

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This book unies the common tensor analytical aspects in engineering and physics. Using tensor analysis enables the reader to understand complex physical phenomena from the basic principles in continuum mechanics including the turbulence, its correlations and modeling to the complex Einstein' tensor equation. The development of General Theory of Relativity and the introduction of spacetime geometry would not have been possible without the use of tensor analysis. This textbook is primarily aimed at students of mechanical, electrical, aerospace, civil and other engineering disciplines as well as of theoretical physics. It also covers the special needs of practicing professionals who perform CFD-simulation on a routine basis and would like to know more about the underlying physics of the commercial codes they use. Furthermore, it is suitable for self-study, provided that the reader has a sufficient knowledge of differential and integral calculus. Particular attention was paid to selecting the application examples. The transformation of Cartesian coordinate system into curvilinear one and the subsequent applications to conservation laws of continuum mechanics and the turbulence physics prepares the reader for fully understanding the Einstein tensor equations, which exhibits one of the most complex tensor equation in theoretical physics.

Mathematics --- Classical mechanics. Field theory --- Fluid mechanics --- Physics --- Applied physical engineering --- toegepaste wiskunde --- economie --- wiskunde --- ingenieurswetenschappen --- fysica --- mechanica --- dynamica --- vloeistoffen --- Tensor products.