the injective tensor product is a particular topological tensor product, a topological vector space (TVS) formed by equipping the tensor product of the...

v\otimes w} is called the tensor product of v and w. An element of V ⊗ W {\displaystyle V\otimes W} is a tensor, and the tensor product of two vectors is sometimes...

injective cross norms. The completions of the resulting topologies on A ⊗ B {\displaystyle A\otimes B} are called the projective and injective tensor...

ϵ Y {\displaystyle X{\widehat {\otimes }}_{\epsilon }Y} , the injective tensor product of the locally convex topological vector spaces (TVSs) X and Y...

In mathematics, the tensor product of two fields is their tensor product as algebras over a common subfield. If no subfield is explicitly specified, the...

In mathematics, the tensor product of modules is a construction that allows arguments about bilinear maps (e.g. multiplication) to be carried out in terms...

{\displaystyle L^{p}(\Omega ,\Sigma ,\mu )\otimes _{\pi }E,} and the injective tensor product, denoted by L p ( Ω , Σ , μ ) ⊗ ε E . {\displaystyle L^{p}(\Omega...

the completion of the injective tensor product (which in this case is identical to the completion of the projective tensor product). The inclusion map In...

completion of the injective tensor product (which in this case is the identical to the completion of the projective tensor product). Tempered distributions...

metric field on M consists of a metric tensor at each point p of M that varies smoothly with p. A metric tensor g is positive-definite if g(v, v) > 0 for...

_{1}\right)} is nuclear, this tensor product is simultaneously the injective tensor product and projective tensor product). In short, the Schwartz kernel...

Inductive tensor product – binary operation on topological vector spacesPages displaying wikidata descriptions as a fallback Injective tensor product Tensor product...

Banach spacePages displaying wikidata descriptions as a fallback Injective tensor product Nuclear operator – Linear operator related to topological vector...

algebraic tensor product X ⊗ Y {\displaystyle X\otimes Y} equipped with the projective tensor norm, and similarly for the injective tensor product X ⊗ ^ ε...

topology Inductive tensor product Injective tensor product Projective tensor product Tensor product of Hilbert spaces Topological tensor product Émery topology...

between the tensor products C ⊗ M → C ⊗ K is injective for every right R-module C. The module M is pure-injective if any pure injective homomorphism...

fallback Injective tensor product Trèves 2006, pp. 412–419. Trèves 2006, pp. 446–451. Diestel, Joe (2008). The Metric Theory of Tensor Products: Grothendieck's...

such that for every C*-algebra B the injective and projective C*-cross norms coincides on the algebraic tensor product A⊗B and the completion of A⊗B with...

mathematics, particularly in algebra, the injective hull (or injective envelope) of a module is both the smallest injective module containing it and the largest...

vector space (TVS) topology on X ⊗ Y , {\displaystyle X\otimes Y,} the tensor product of two locally convex TVSs, making the canonical map ⋅ ⊗ ⋅ : X × Y →...

K(X) of compact operators on X is isometrically isomorphic to the injective tensor product X ′ ⊗ ^ ε X ≃ K ( X ) . {\displaystyle X'{\widehat {\otimes }}_{\varepsilon...

flat if taking the tensor product over R with M preserves exact sequences. A module is faithfully flat if taking the tensor product with a sequence produces...

provide a basis for the cotangent space at p. The tensor product (denoted by the symbol ⊗) yields a tensor field of type (0, 2), i.e. the type that expects...

manifold to another is a map which pulls back the metric tensor on the second manifold to the metric tensor on the first. When such a map is also a diffeomorphism...

Inductive tensor product – binary operation on topological vector spacesPages displaying wikidata descriptions as a fallback Injective tensor product Locally...

with tensor order, which is called tensor rank. Tensor order is the number of indices required to write a tensor, and thus matrices all have tensor order...

flat modules. Similarly every module has injective resolutions, which are right resolutions consisting of injective modules. Given a module M over a ring...

completions, the completions of topological tensor products, such as projective tensor products or injective tensor products, of the Banach space ℓ 1 ( S ) {\displaystyle...

(the injective homomorphism V → V ∗ {\displaystyle V\to V^{*}} ) and thus hold more generally. The term "inner product" is opposed to outer product (tensor...

actions of countable amenable groups on probability spaces. The infinite tensor product of a countable number of factors of type In with respect to their tracial...