Banach Modules and Functors on Categories of Banach Spaces |
Contents
The categories Ban and | 1 |
Tensor products of Banach spaces | 47 |
Banach modules | 99 |
Copyright | |
5 other sections not shown
Common terms and phrases
A-bimodule approximate identity approximate unit Ban Ban Banach algebra Banach modules Banach space bifunctor bifunctor G bilinear bimodule bounded linear maps canonical map categories of Banach closed subspace coincides colimits commutes compact convergence Consequently consider contra-covariant contravariant functors convex Corollary corresponding covariant functor defined Definition denote dense DF(X diagram dual space duality easily seen element equation essential exists F₁ follows forgetful functor functional functor F G₁ given H₁ homomorphism I₁ implies injective isometric isomorphism isometrically contained left A-module left adjoint Lemma map f metric approximation property mono morphism Nat F,G Nat G natural transformation norm projective tensor product Proof Proposition quotient map right A-module satisfies sequence space subcategories of Ban subfunctor subset tensor product theorem theory topology of compact V₁ w*-dense Waelbroeck space weak retract x₁ y₁