Hilbert {$C\sp *$}-module representation on Haagerup tensor products and group systems

Fuzzy projective modules and tensor products in fuzzy module categories

Let $R$ be a commutative ring. We write $mbox{Hom}(mu_A, nu_B)$ for the set of all fuzzy $R$-morphisms from $mu_A$ to $nu_B$, where $mu_A$ and $nu_B$ are two fuzzy $R$-modules. We make$mbox{Hom}(mu_A, nu_B)$ into fuzzy $R$-module by redefining a function $alpha:mbox{Hom}(mu_A, nu_B)longrightarrow [0,1]$. We study the properties of the functor $mbox{Hom}(mu_A,-):FRmbox{-Mod}rightarrow FRmbox{-Mo...

The Haagerup Invariant for Tensor Products of Operator Spaces

Hilbert-Schmidt operators and tensor products of Hilbert spaces

Let V ⊗HS W be the completion of V ⊗alg W in the norm defined by this inner product. V ⊗HS W is a Hilbert space; however, as Garrett shows it is not a categorical tensor product, and in fact if V and W are Hilbert spaces there is no Hilbert space that is their categorical tensor product. (We use the subscript HS because soon we will show that V ⊗HS W is isomorphic as a Hilbert space to the Hilb...

fuzzy projective modules and tensor products in fuzzy module categories

let $r$ be a commutative ring. we write $mbox{hom}(mu_a, nu_b)$ for the set of all fuzzy $r$-morphisms from $mu_a$ to $nu_b$, where $mu_a$ and $nu_b$ are two fuzzy $r$-modules. we make$mbox{hom}(mu_a, nu_b)$ into fuzzy $r$-module by redefining a function $alpha:mbox{hom}(mu_a, nu_b)longrightarrow [0,1]$. we study the properties of the functor $mbox{hom}(mu_a,-):frmbox{-mod}rightarrow frmbox{-mo...

Inner Products and Module Maps of Hilbert C∗-modules

Let E and F be two Hilbert C∗-modules over C∗-algebras A and B, respectively. Let T be a surjective linear isometry from E onto F and φ a map from A into B. We will prove in this paper that if the C∗-algebras A and B are commutative, then T preserves the inner products and T is a module map, i.e., there exists a ∗-isomorphism φ between the C∗-algebras such that 〈Tx, Ty〉 = φ(〈x, y〉), and T (xa) ...