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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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        3
        votes
        1answer
        70 views

        Graded adjointable operators on a graded Hilbert space

        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 ...
        1
        vote
        1answer
        76 views

        Extending $C^*$-norms from $*$-subalgebras

        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 $\...
        3
        votes
        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 $C^*(X,\alpha)$...
        2
        votes
        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 ...
        2
        votes
        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 ...
        6
        votes
        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}...
        2
        votes
        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^{*} - (...
        5
        votes
        2answers
        126 views

        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 ...
        1
        vote
        0answers
        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.
        5
        votes
        1answer
        199 views

        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 ...
        1
        vote
        1answer
        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 ...
        3
        votes
        1answer
        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 ...
        9
        votes
        0answers
        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-...
        3
        votes
        1answer
        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?
        5
        votes
        1answer
        120 views

        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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