We consider the ideal structure of a reduced crossed product unital C∗-algebra equipped with an action discrete group. More specifically we find sufficient and necessary conditions for group to have intersection property, meaning that non-zero ideals in restrict underlying C∗-algebra. show property on is equivalent equivariant injective envelope. also centre envelope always contains C∗-algebrai...

(ii) Denote this map by φ, which is induced by the compositions with εi : Xi ↪→ ⊔ j Xj , i ∈ I. If φ(fi) = φ(gj) for some fi ∈ Hom(Y,Xi) and gj ∈ Hom(Y,Xj), then we must have i = j because φ(fi) and φ(gj) have the same image. Since φ(fi) = εi ◦ fi, φ(gi) = εi ◦ gi and εi is an injective map, we deduce that fi(y) = gi(y), ∀y ∈ Y , i.e. fi = gi. (iii) This map is induced by the composition with t...

In this paper we prove that the 3-fold injective tensor product ℓ1⊗ˆεℓ1⊗ˆεℓ1 is not isomorphic to any subspace of ℓ1⊗ˆεℓ1. This result provides a new solution problem Diestel on projective products c0. Moreover, implies for infinite countable compact metric space K, C(K)⊗ˆπC(K)⊗ˆπC(K) quotient C(K)⊗ˆπC(K).

Codes Description of C Nonsingular C injective – i.e. ∀x, x′ ∈ X , x 6= x′ =⇒ C(x) = C(x′) Uniquely Decodable The extension the code is nonsingular. Prefix/Instantaneous/Self-punctuating No code word prefixes another: for all distinct x′, x′′ ∈ X , C(x′) does not start with C(x′′) We illustrate this below with the following example for the symbols {a, b, c, d} taken from Chapter 5 in Cover and ...

Isbell and Semadeni [Trans. Amer. Math. Soc. 107 (1963)] proved that every infinite-dimensional $1$-injective Banach space contains a hyperplane is $(2+\varepsilon )$-injective for $\varepsilon \gt 0$, yet not $2$-injective, rem

We prove that in the space of all Cr (r ≥ 1) partially hyperbolic diffeomorphisms, there is a C1 open and dense set of accessible diffeomorphisms. This settles the C1 case of a conjecture of Pugh and Shub. The same result holds in the space of volume preserving or symplectic partially hyperbolic diffeomorphisms. Combining this theorem with results in [Br], [Ar] and [PugSh3], we obtain several c...

LetR be a ring andM a rightR-module with S= End(MR). The moduleM is called almost principally quasi-injective (or APQ-injective for short) if, for any m∈M, there exists an S-submodule Xm of M such that lMrR(m) = Sm ⊕ Xm. The module M is called almost quasiprincipally injective (or AQP-injective for short) if, for any s∈ S, there exists a left ideal Xs of S such that lS(ker(s)) = Ss ⊕ Xs. In thi...