Related papers: Projections in Rotation Algebras and Theta Functio…

The rotation algebra $\mathcal A_{\theta}$ is the universal $C^*$--algebra generated by unitary operators $U, V$ satisfying the commutation relation $UV = \omega V U$ where $\omega= e^{2\pi i \theta}.$ They are rational if $\theta = p/q$…

We compute the semiflat positive cone $K_0^{+SF}(A_\theta^\sigma)$ of the $K_0$-group of the irrational rotation orbifold $A_\theta^\sigma$ under the noncommutative Fourier transform $\sigma$ and show that it is determined by classes of…

Projections are constructed in the rotation algebra that are orthogonal to their Fourier transform and which are fixed under the flip automorphism. Such projections are expected in a construction of an inductive limit structure for the…

We introduce a class of generalized universal irrational rotation $C^*$-algebras $A_{\theta,\gamma}=C^*(x,w)$ which is characterized by the relations $w^*w=ww^*=1$, $x^*x=\gamma(w)$, $xx^*=\gamma(e^{-2\pi i\theta}w)$, and $xw=e^{-2\pi…

For any irrational theta and rational number p/q such that q|qtheta-p|<1, a projection e of trace q|qtheta-p| is constructed in the the irrational rotation algebra A_theta that is invariant under the Fourier transform. (The latter is the…

It is shown that for any approximately central (AC) projection $e$ in the Flip orbifold $A_\theta^\Phi$ (of the irrational rotation C*-algebra $A_\theta$), and any modular automorphism $\alpha$ (arising from SL$(2,\mathbb Z)$), the AC…

We found that if $u$ and $v$ are any two unitaries in a unital $C^*$-algebra with $\|uv-vu\|<2$ such that $uvu^*v^*$ commutes with $u$ and $v,$ then the \SCA\, $A_{u,v}$ generated by $u$ and $v$ is isomorphic to a quotient of the rotation…

We investigate a set of functional equations defining a projection in the noncommutative 2-torus algebra $A_{\theta}$. The exact solutions of these provide various generalisations of the Powers-Rieffel projection. By identifying the…

In the theory of C*-algebras, interesting noncommutative structures arise as deformations of the tensor product. For instance, the rotation algebra may be seen as a scalar twist deformation of the tensor product of the functions on the…

Frames on Hilbert C*-modules have been defined for unital C*-algebras by Frank and Larson and operator valued frames on a Hilbert space have been studied in arXiv.0707.3272v1.[math.FA]. Goal of the present paper is to introduce operator…

We solve a class of lifting problems involving approximate polynomial relations (soft polynomial relations). Various associated C*-algebras are therefore projective. The technical lemma we need is a new manifestation of Akemann and…

Halmos' two projections theorem for Hilbert space operators is one of the fundamental results in operator theory. In this paper, we introduce the term of two harmonious projections in the context of adjointable operators on Hilbert…

Let A be a C*-algebra and A** its enveloping von Neumann algebra. C. Akemann suggested a kind of non-commutative topology in which certain projections in A** play the role of open sets. The adjectives "open", "closed", "compact", and…

We show that every point $x_0\in [0,1]$ carries a representation of a $C^*$-algebra that encodes the orbit structure of the linear mod 1 interval map $f_{\beta,\alpha}(x)=\beta x +\alpha$. Such $C^*$-algebra is generated by partial…

With an action $\alpha$ of $\mathbb{R}^n$ on a $C^*$-algebra $A$ and a skew-symmetric $n\times n$ matrix $\Theta$ one can consider the Rieffel deformation $A_\Theta$ of $A$, which is a $C^*$-algebra generated by the $\alpha$-smooth elements…

The classical Gelfand--Naimark theorems provide important insight into the structure of general and of commutative C*-algebras. It is shown that these can be generalized to certain ordered *-algebras. More precisely, for $\sigma$-bounded…

We define a strong Morita-type equivalence $\sim _{\sigma \Delta }$ for operator algebras. We prove that $A\sim _{\sigma \Delta }B$ if and only if $A$ and $B$ are stably isomorphic. We also define a relation $\subset _{\sigma \Delta }$ for…

We develop some tools for manipulating and constructing projections in C*-algebras. These are then applied to give short proofs of some standard projection homotopy results, as well as strengthen some fundamental classical results for…

We investigate the deformation of involution and multiplication in a unital $C^*$-algebra when its norm is fixed. Our main result is to present all multiplications and involutions on a given $C^*$-algebra $\mathcal{A}$ under which…

We describe absolutely ordered $p$-normed spaces, for $1 \le p \le \infty$ which presents a model for "non-commutative" vector lattices and includes order theoretic orthogonality. To demonstrate its relevance, we introduce the notion of…