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# Questions tagged [c-star-algebras]

A C*-algebra is a complex Banach algebra together with an isometric antilinear involution satisfying (a?b)* = b*?a* and the C*-identity ‖a*?a‖ = ‖a‖². Related tags: [tag:banach-algebras], [tag:von-neumann-algebras], [tag:operator-algebras], [tag:spectral-theory].

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Given a graded Hilbert space $\mathbf{H} = \bigoplus_{k \in \mathbb{N}} \mathbf{H}_k$, one might extend the notion of adjoint to a "graded adjoint" defined as follows: $L \in B(\mathbf{H})$ is said to ...
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Let $A$ be a unital $*$-algebra, and $B$ a unital $*$-subalgebra of $A$. In addition, assume that there exists a $B$-$B$-sub-bimodule $C \subset A$, such that $$A \simeq B \oplus C,$$ where $\... 0answers 42 views ### The number of minimal components of a dynamical system via certain invariants of corresponding cross product$C^*$algebra, some precise examples Let$X$be a compact Hausdorff space and$\alpha$be a homeomorphism of$X$. So we have a natural action of$\mathbb{Z}$on$C(X)$which generates the cross product algebra$C^*(X,\alpha)$... 0answers 70 views ### Invertibility modulo the intersection of ideals in$C^*$-algebras This is a crosspost from math.se because it did not get any attention whatsoever. I therefore assume that it fits here better. Let$\mathcal{A}$be a$C^*$-algebra and$A \in \mathcal{A}$. I am ... 1answer 119 views ### Does the square root of a finite propagation operator have finite propagation? Let$X$be a non-compact manifold and let$C_0(X)$act on$L^2(X)$by pointwise multiplication. We say$T\in\mathcal{B}(L^2(X))$has finite propagation if there exists an$r>0$such that: for all ... 1answer 76 views ### Tensoring adjointable maps on Hilbert modules Given a right Hilbert$A$-module$E$, and a right Hilbert$B$-module$F$, together with non-degenerate$*$-homomorphism$\phi:A \to \mathcal{L}_B(F)$, we can form the tensor product$$E \otimes_{\phi}... 1answer 69 views ### Twisted canonical commutation relations I am dealing with universal C*-algebra generated by$x,y$with the following relations:$xy = qyx$,$x^{*}y = qyx^{*}$,$y^{*}x = qxy^{*}$,$x^{*}x = q^2xx^{*} - (1-q^2)yy^{*}$,$y^{*}y = q^2yy^{*} - (...
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### Finite-dimensional Hilbert $C^*$-modules

Does there exist a classification, or characterization, of finite-dimensional Hilbert $C^*$-modules? More generally, does there exist a characterization of countable direct sums of finite-dimensional ...
129 views

### A criterion for abelian $C^*$ algebra [closed]

Let $A$ be a unital $C^*$ algebra such that for any two positive elements $x$, $y$ in $A$, whenever $x\leq y$ we have that $x^2\leq y^2$. Prove that $A$ is abelian.
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### Variations on Kaplansky Density

Let $A$ be a $C^*$-algebra and $\pi:A\rightarrow B(H)$ a faithful $*$-representation, so $M=\pi(A)''$ is a von Neumann algebra and $A\rightarrow M$ is an inclusion. von Neumann's Bicommutant Theorem ...
137 views

### Projections in CAR (Canonical Anticommutation Relation) algebra

How does one show that the projections in the [CAR algebra][1] do not form a complete lattice? Background info: my paper with Scholz [2] paper works in the (infinite) CAR algebra and tries to ...
126 views

### On crossed product subalgebra

For Compact pmp actions of a group $G$ on measure space $(X,\mu)$, if a subalgebra $B$ is such that $L(G)\subset B \subset L^{\infty}(X)\rtimes G$, is it always true that $B$ is also of the form ...
157 views

### Geometric motivation behind the Fredholm module definition

If $A$ is an involutive algebra over the complex numbers $\mathbb{C}$, then a Fredholm module over $A$ consists of an involutive representation of $A$ on a Hilbert space $H$, together with a self-...
137 views

### Noncommutative Leray - Hirsch theorem in the context of noncommutative principal bundles

In the literature, are there some researchs on non commutative analogy of Leray-Hirsch theorem in the context of non commutative Principal bundles?
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### A sequence of points in the spectrum of a subhomogeneous C$^{*}$-algebra can converge to at most finitely many points

Let $A$ be a subhomogeneous C$^{*}$-algebra (i.e., there is a finite upper bound on the size of the irreducible representations of $A$). Let $\hat{A}$ denote its spectrum. I heard of a result that ...

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