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Kamran Sharifi

  1. The product of operators with closed range in Hilbert C*-modules.

    Пнд, 10/25/2010 - 15:01 — SomNambul
    Authors: Kamran Sharifi
    Subjects: Operator Algebras
    Abstract

    The Dixmier (or minimal) angle between submodules $M$ and $N$ of a Hilbert
    C*-module $E$ is the angle $\alpha_0 (M,N)$ in $[0, \pi /2]$ whose cosine is
    defined by $c_0(M,N)= {\rm sup} \{\| <x,y> \| : x \in M, \|x\| \leq 1 \, , y
    \in N, \|y\| \leq 1 \}.$ Suppose $T$ and $S$ are bounded adjointable operators
    with close range between Hilbert C*-modules, then $TS$ has closed range if and
    only if $Ker(T)+Ran(S)$ is an orthogonal summand, if and only if
    $Ker(S^*)+Ran(T^*)$ is an orthogonal summand.

  2. Adjointability of densely defined closed operators and the Magajna-Schweizer Theorem.

    Пнд, 01/25/2010 - 16:01 — SomNambul
    Authors: Michael Frank, Kamran Sharifi
    Subjects: Operator Algebras
    Abstract

    In this notes unbounded regular operators on Hilbert $C^*$-modules over
    arbitrary $C^*$-algebras are discussed. A densely defined operator $t$
    possesses an adjoint operator if the graph of $t$ is an orthogonal summand.
    Moreover, for a densely defined operator $t$ the graph of $t$ is orthogonally
    complemented and the range of $P_FP_{G(t)^\bot}$ is dense in its biorthogonal
    complement if and only if $t$ is regular.

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