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1. CMB 2010 (vol 54 pp. 141)
Linear Maps on $C^*$-Algebras Preserving the Set of Operators that are Invertible in $\mathcal{A}/\mathcal{I}$ |
Linear Maps on $C^*$-Algebras Preserving the Set of Operators that are Invertible in $\mathcal{A}/\mathcal{I}$
For $C^*$-algebras $\mathcal{A}$ of real rank zero, we describe
linear maps $\phi$ on $\mathcal{A}$ that are surjective up to ideals
$\mathcal{I}$, and $\pi(A)$ is invertible in $\mathcal{A}/\mathcal{I}$ if and only if
$\pi(\phi(A))$ is invertible in $\mathcal{A}/\mathcal{I}$, where $A\in\mathcal{A}$ and
$\pi:\mathcal{A}\to\mathcal{A}/\mathcal{I}$ is the quotient map. We also consider similar
linear maps preserving zero products on the Calkin algebra.
Keywords:preservers, Jordan automorphisms, invertible operators, zero products Categories:47B48, 47A10, 46H10 |
2. CMB 2009 (vol 52 pp. 535)
A Note on Locally Nilpotent Derivations\\ and Variables of $k[X,Y,Z]$ We strengthen certain results
concerning actions of $(\Comp,+)$ on $\Comp^{3}$
and embeddings of $\Comp^{2}$ in $\Comp^{3}$,
and show that these results are in fact valid
over any field of characteristic zero.
Keywords:locally nilpotent derivations, group actions, polynomial automorphisms, variable, affine space Categories:14R10, 14R20, 14R25, 13N15 |
3. CMB 2008 (vol 51 pp. 481)
Universal Inner Functions on the Ball It is shown that given any sequence of automorphisms $(\phi_k)_k$ of the
unit ball $\bn$ of $\cn$ such that $\|\phi_k(0)\|$ tends to $1$,
there exists an inner function
$I$ such that the family of ``non-Euclidean translates"
$(I\circ\phi_k)_k$ is locally uniformly dense in the unit ball of
$H^\infty(\bn)$.
Keywords:inner functions, automorphisms of the ball, universality Categories:32A35, 30D50, 47B38 |
4. CMB 2008 (vol 51 pp. 261)
On the Classification of Rational Quantum Tori and the Structure of Their Automorphism Groups An $n$-dimensional quantum torus is a twisted group algebra of the
group $\Z^n$. It is called rational if all invertible commutators are roots
of unity. In the present note we describe a normal form for rational
$n$-dimensional quantum
tori over any field. Moreover, we show that for
$n = 2$ the natural exact sequence
describing the automorphism group of the quantum torus splits over any
field.
Keywords:quantum torus, normal form, automorphisms of quantum tori Category:16S35 |