In this article, we will give a characterization of Banach bimodules over C∗-algebras of compact operators that arises from operator spaces as well as a characterization of (F)-Banach bundles amongst all (H)-Banach bundles over a hyper-Stonian space. These two characterizations are concerned with whether certain natural map from a Banach bimodule to its canonical bidual is isometric (we call su...

Let R and S be arbitrary associative rings. Given a bimodule RWS , we denote by ∆? and Γ? the functors Hom?(−, W ) and Ext?(−, W ), where ? = R or S. We say that RWS is a finitistic weakly cotilting bimodule (briefly FWC) if for each module M cogenerated by W , finitely generated or homomorphic image of a finite direct sum of copies of W , ΓM = 0 = Ext(M, W ). We are able to describe, on a larg...

An dimensional crossed cube, CQ,,, is a variation of hypercubes. in this paper, we give a new shortest path routing algorithm based on a new distance measure defined hsreln. In comparison with Efe's algorithm, which generates one shortest path in O(ri2) time, our algorithm can generate more shortest paths in O ( n ) time. Based on a given shortest path routing algorithm, we consider a new perfo...

In this paper the Hochschild-cochain-complex of an A∞-algebra A with values in an A∞-bimodule M over A and maps between them is defined. Then, an∞-inner-product on A is defined to be an A∞-bimodule-map between A and its dual A∗. There is a graph-complex associated to A∞-algebras with ∞-inner-product.

1ICFO-Institut de Ciencies Fotoniques, and Universitat Politecnica de Catalunya, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain 2Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow Region, 142190, Russia 3Centro de Física Teórica e Computacional and Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Campo Grande 2, Edifício C8, Lisb...

For dynamical systems defined by a covering map of a compact Hausdorff space and the corresponding transfer operator, the associated crossed product C∗-algebras C(X) ⋊α,L N introduced by Exel and Vershik are considered. An important property for homeomorphism dynamical systems is topological freeness. It can be extended in a natural way to in general non-invertible dynamical systems generated b...

We study charge transport through a topological superconductor with a pair of Majorana end states coupled to leads via quantum dots with resonant levels. The nonlocality of the Majorana bound states opens the possibility of crossed Andreev reflection with nonlocal shot noise due to the injection of an electron into one end of the superconductor followed by the emission of a hole at the other en...

The results of a previous paper on the equivariant homotopy theory of crossed complexes are generalised from the case of a discrete group to general topological groups. The principal new ingredient necessary for this is an analysis of homotopy coherence theory for crossed complexes, using detailed results on the appropriate Eilenberg–Zilber theory, and of its relation to simplicial homotopy coh...