We study the theory of a Hilbert space H as a module for a unital C∗-algebra A from the point of view of continuous logic. We show this theory, in an appropiate lenguage, has quantifier elimination and it is superstable. We show that for every v ∈ H the type tp(v/∅) is in correspondence with the positive linear functional over A defined by v. Finally, we characterize forking, orthogonality and ...

A semiregular operator on a Hilbert C∗-module, or equivalently, on the C∗-algebra of ‘compact’ operators on it, is a closable densely defined operator whose adjoint is also densely defined. It is shown that for operators on extensions of compacts by unital or abelian C∗-algebras, semiregularity leads to regularity. Two examples coming from quantum groups are discussed. AMS Subject Classificatio...

Mathieu and Ruddy proved that if be a unital spectral isometry from a unital C*-algebra Aonto a unital type I C*-algebra B whose primitive ideal space is Hausdorff and totallydisconnected, then is Jordan isomorphism. The aim of this note is to show that if be asurjective spectrum preserving additive map, then is a Jordan isomorphism without the extraassumption totally disconnected.

If R is a commutative unital ring and M R-module, then each element of EndR(M) determines left EndR(M)[X]-module structure on EndR(M), where the R-algebra endomorphisms EndR(M)[X]=EndR(M)⊗RR[X]. These structures provide very short proof Cayley-Hamilton theorem, which may be viewed as reformulation in Algebra by Serge Lang. Some generalisations theorem can easily proved using proposed method.

In this work, all rings under consideration will be assumed to commutative with nonzero identity and modules unital. We introduce the concept of Restrict Nearly primary finitely compactly packed modules, which generalizes modules. find conditions that make packed. Also, several results on are proved. addition, necessary sufficient for an ℛ−module

There is growing evidence that Hilbert C*-module theory and the theory of wavelets and Gabor (i.e. Weyl-Heisenberg) frames are tightly related to each other in many aspects. Both the research fields can benefit from achievements of the other field. The goal of the talk given at the mini-workshop was to give an introduction to the theory of module frames and to Hilbert C*modules showing key anal...

let a be a unital r-algebra and m be a unital a-bimodule. it is shown that every jordan derivation of the trivial extension of a by m, under some conditions, is the sum of a derivation and an antiderivation.

In this paper, all rings are associative with identity and all modules are unital left modules unless otherwise specified. Let R be a ring and M a module. N ≤M will mean N is a submodule of M. A submodule E of M is called essential in M (notation E ≤e M) if E∩A = 0 for any nonzero submodule A of M. Dually, a submodule S of M is called small in M (notation S M) if M = S+T for any proper submodul...

It is shown that every  almost linear bijection $h : Arightarrow B$ of a unital $C^*$-algebra $A$ onto a unital$C^*$-algebra $B$ is a $C^*$-algebra isomorphism when $h(3^n u y) = h(3^n u) h(y)$ for allunitaries  $u in A$, all $y in A$, and all $nin mathbb Z$, andthat almost linear continuous bijection $h : A rightarrow B$ of aunital $C^*$-algebra $A$ of real rank zero onto a unital$C^*$-algebra...