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        Questions tagged [oa.operator-algebras]

        Algebras of operators on Hilbert space, $C^*-$algebras, von Neumann algebras, non-commutative geometry

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        votes
        1answer
        31 views

        Trace class operators in the unit ball of a finite dimensional subvector space of $B(H)$

        Let $F\subset B(H)$ be a finite dimensional subvector space of the space of all bounded operators on a Hilbert space. Question: Is there an upper bound for $$\{|tr(T)| \text{where} \quad T\in ...
        3
        votes
        0answers
        23 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 ...
        5
        votes
        2answers
        257 views

        Non-standard tensor products of inner product spaces

        For two inner product spaces $(\mathcal{V}, (\cdot,\cdot)_V)$ and $(\mathcal{W}, (\cdot,\cdot)_W)$, we can put an inner product on their tensor product in the obvious way: $$ (1) ~~~~ \langle v \...
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        votes
        0answers
        60 views

        Examples of a full Hilbert C(X)-bimodule E such that the crossed product $C(X) \rtimes_E \mathbb{Z}$ is simple?

        Let $A = C(X)$ be a commutative $C^*$-algebra. An example of a full finitely generated Hilbert $A$-bimodule E such that the crossed product $C(X) \rtimes_E \mathbb{Z}$, as defined by Abadie, Eilers ...
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        votes
        0answers
        84 views

        Textbook covering superoperators and tensor products

        I am looking for a textbook to cover the following tensor product (and, of course, the theory around it): Let $\otimes_1$ denote the tensor product on Hilbert spaces. Let $\otimes_2$ denote the ...
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        85 views
        +50

        The tower of path algebras associated to a tower of finite dimensional $C^*$-algebras is isomorphic to the original tower

        Let $A_0\subseteq A_1\subseteq...$ be an infinite tower of unital inclusions of finite dimensional $C^*$-algebras and $B_0\subseteq B_1\subseteq ...$ be its associated infinite tower of path algebras. ...
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        0answers
        64 views

        Characterzing compact actions on von Neumann algebra

        Suppose $G$ is a countable discrete group acting on vN algebra $M$, the action is compact. Can we have a topology on Aut$(M)$ such that $\{\sigma_{g}\in \text{Aut}(M):g \in G\}$ form a compact subset ...
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        votes
        1answer
        152 views

        A spectral description of Fredholm operators

        Let $L:H \to H$ be a bounded operator on a Hilbert space $H$, with finite dimensional kernel, and whose adjoint also has finite dimensional kernel. Is it true that $L$ is Fredholm if and only if its ...
        4
        votes
        0answers
        100 views

        Contractible Banach algebras

        A Banach algebra $A$ is contractible if $H^1(A, X)=0$ for all Banach $A$-bimodules $X$. Now to my question Let $A$ be Banach algebra and $I$ be closed ideal of $A$. If $I$ and $A/I$ are both ...
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        vote
        1answer
        277 views

        Recovering “$n$” from $M_n(\mathbb{C})$

        Is there an example of an infinite-dimensional $C^*$-algebra $A$ which admits the following structure: The $C^*$ algebra $A$ admits a faithful trace $tr$ such that the multiplication $m: A\otimes A \...
        3
        votes
        1answer
        120 views

        Residually finite-dimensional $C^*$-algebra

        Suppose $A$ is a non-unital residually finite-dimensional (RFD) $C^*$-algebra, then the multiplier algebra $M(A)$ is also RFD. I wonder whether there exists a trace on the corona algebra $M(A)/A$?
        4
        votes
        0answers
        38 views

        Commuting flows problem for non-Lipschitz vector fields

        Let $X$ be a continuous vector field on a (say compact) manifold $M$, if $X$ has ODE uniqueness then we can define its associated flow $\mathcal F_X:\mathbb R\times M\to M$ uniquely given by $\mathcal ...
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        votes
        0answers
        77 views

        Enveloping von Neumann algebra of Clifford algebra

        As explained in the book "Spinors in Hilbert Space" by Plymen and Robinson, if $V$ is a complex (separable) Hilbert space with a real structure, and $\mathrm{Cl}(V)$ the corresponding Clifford algebra,...
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        0answers
        46 views

        On cyclicity of a module

        Let $A$ be a $\text{ von Neumann algebra }$, $\mathcal{H}$ is a cyclic $A$ module, $G$ be a finite group acting on $A$, is $\mathcal{H}$ cyclic module over fixed point subalgebra of the action? ...
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        0answers
        55 views

        On existence of sequence of unitaries in $II_{1}$ factor $M$

        Let $M$ be a $\mathrm{II}_{1}$ factor acting on $L^{2}(M, \tau)$ in standard form, let $\{e_{n}:n \in \mathbb{N}\}$ be fixed orthonormal basis of $L^{2}(M, \tau)$, does there exist sequence of ...

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