Abstract We consider two inclusions of $C^{*}$ -algebras whose small have approximate units the large and their spaces all bounded bimodule linear maps. suppose that are strongly Morita equivalent. In this paper, we shall show there exists an isometric isomorphism from one maps to other space study basic properties about isomorphism. And, using isomorphism, define Picard group for a map discuss...

We give an analogue of the classical exponential map on Lie groups for Hopf $*$-algebras with differential calculus. The major difference case is interpretation value map, classically element group. interpretations as states algebra, elements a Hilbert $C^{*} $-bimodule $\frac{1}{2}$ densities and dual algebra. examples complex valued functions $S_{3}$ $\mathbb{Z}$, Woronowicz's matrix quantum ...

A unital Fréchet algebra A is called contractible if there exists an element d ∈ A⊗̂A such that πA(d) = 1 and ad = da for all a ∈ A where πA : A⊗̂A → A is the canonical Fréchet A-bimodule morphism. We give a sufficient condition for an infinite-dimensional contractible Fréchet algebra A to be a direct sum of a finite-dimensional semisimple algebra M and a contractible Fréchet algebra N without an...

We study the quantum Riemannian geometry of projective spaces any dimension. In particular, we compute Riemann and Ricci tensors using previously introduced metrics Levi-Civita connections. show that tensor is a bimodule map derive various consequences this fact. prove proportional to metric, giving analogue Einstein condition, corresponding scalar curvature.

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...

We construct a counterexample to Solel’s[25] conjecture that the range of any contractive, idempotent, MASA bimodule map on B(H) is necessarily a ternary subalgebra. Our construction reduces this problem to an analogous problem about the ranges of idempotent maps that are equivariant with respect to a group action. Such maps are important to understand Hamana’s theory of G-injective operator sp...

To a B-coring and a (B, A)-bimodule that is finitely generated and projective as a right A-module an A-coring is associated. This new coring is termed a base ring extension of a coring by a module. We study how the properties of a bimodule such as separability and the Frobenius properties are reflected in the induced base ring extension coring. Any bimodule that is finitely generated and projec...

To a B-coring and a (B, A)-bimodule that is finitely generated and projective as a right A-module an A-coring is associated. This new coring is termed a base ring extension of a coring by a module. We study how the properties of a bimodule such as separability and the Frobenius properties are reflected in the induced base ring extension coring. Any bimodule that is finitely generated and projec...