1. CMB 2012 (vol 57 pp. 37)
 Dashti, Mahshid; NasrIsfahani, Rasoul; Renani, Sima Soltani

Character Amenability of Lipschitz Algebras
Let ${\mathcal X}$ be a locally compact metric space and let
${\mathcal A}$ be any of the Lipschitz algebras
${\operatorname{Lip}_{\alpha}{\mathcal X}}$, ${\operatorname{lip}_{\alpha}{\mathcal X}}$ or
${\operatorname{lip}_{\alpha}^0{\mathcal X}}$. In this paper, we show, as a
consequence of rather more general results on Banach algebras,
that ${\mathcal A}$ is $C$character amenable if and only if
${\mathcal X}$ is uniformly discrete.
Keywords:character amenable, character contractible, Lipschitz algebras, spectrum Categories:43A07, 46H05, 46J10 

2. CMB 2012 (vol 57 pp. 145)
 Mustafayev, H. S.

The Essential Spectrum of the Essentially Isometric Operator
Let $T$ be a contraction on a complex, separable, infinite dimensional
Hilbert space and let $\sigma \left( T\right) $ (resp. $\sigma _{e}\left(
T\right) )$ be its spectrum (resp. essential spectrum). We assume that $T$
is an essentially isometric operator, that is $I_{H}T^{\ast }T$ is compact.
We show that if $D\diagdown \sigma \left( T\right) \neq \emptyset ,$ then
for every $f$ from the discalgebra,
\begin{equation*}
\sigma _{e}\left( f\left( T\right) \right) =f\left( \sigma _{e}\left(
T\right) \right) ,
\end{equation*}
where $D$ is the open unit disc. In addition, if $T$ lies in the class
$ C_{0\cdot }\cup C_{\cdot 0},$ then
\begin{equation*}
\sigma _{e}\left( f\left( T\right) \right) =f\left( \sigma \left( T\right)
\cap \Gamma \right) ,
\end{equation*}
where $\Gamma $ is the unit circle. Some related problems are also discussed.
Keywords:Hilbert space, contraction, essentially isometric operator, (essential) spectrum, functional calculus Categories:47A10, 47A53, 47A60, 47B07 

3. CMB 2009 (vol 52 pp. 66)
 Dryden, Emily B.; Strohmaier, Alexander

Huber's Theorem for Hyperbolic Orbisurfaces
We show that for compact orientable hyperbolic orbisurfaces, the
Laplace spectrum determines the length spectrum as well as the
number of singular points of a given order. The converse also holds, giving
a full generalization of Huber's theorem to the setting of
compact orientable hyperbolic orbisurfaces.
Keywords:Huber's theorem, length spectrum, isospectral, orbisurfaces Categories:58J53, 11F72 

4. CMB 2000 (vol 43 pp. 51)
 Edward, Julian

Eigenfunction Decay For the Neumann Laplacian on HornLike Domains
The growth properties at infinity for eigenfunctions corresponding to
embedded eigenvalues of the Neumann Laplacian on hornlike domains
are studied. For domains that pinch at polynomial rate, it is shown
that the eigenfunctions vanish at infinity faster than the reciprocal
of any polynomial. For a class of domains that pinch at an exponential
rate, weaker, $L^2$ bounds are proven. A corollary is that eigenvalues
can accumulate only at zero or infinity.
Keywords:Neumann Laplacian, hornlike domain, spectrum Categories:35P25, 58G25 

5. CMB 1998 (vol 41 pp. 196)
 Nakazi, Takahiko

BrownHalmos type theorems of weighted Toeplitz operators
The spectra of the Toeplitz operators on the weighted Hardy space
$H^2(Wd\th/2\pi)$ and the Hardy space $H^p(d\th/2\pi)$, and the
singular integral operators on the Lebesgue space $L^2(d\th/2\pi)$
are studied. For example, the theorems of BrownHalmos type and
HartmanWintner type are studied.
Keywords:Toeplitz operator, singular integral, operator, weighted Hardy space, spectrum. Category:47B35 
