101. CMB 1998 (vol 41 pp. 413)
 LlorensFuster, Enrique; Sims, Brailey

The fixed point property in $\lowercase{c_0}$
A closed convex subset of $c_0$ has the fixed point property
($\fpp$) if every nonexpansive self mapping of it has a fixed
point. All nonempty weak compact convex subsets of $c_0$ are
known to have the $\fpp$. We show that closed convex subsets
with a nonempty interior and nonempty convex subsets which are
compact in a topology slightly coarser than the weak topology
may fail to have the $\fpp$.
Categories:47H09, 47H10 

102. CMB 1998 (vol 41 pp. 434)
103. CMB 1998 (vol 41 pp. 298)
 Jahandideh, M. T.

On the idealtriangularizability of semigroups of quasinilpotent positive operators on $C({\cal K})$
It is known that a semigroup of quasinilpotent integral operators,
with positive lower semicontinuous kernels, on $L^2( X, \mu)$,
where $X$ is a locally compact HausdorffLindel\"of space and $\mu$
is a $\sigma$finite regular Borel measure on $X$, is
triangularizable. In this article we use the Banach lattice version
of triangularizability to establish the idealtriangularizability
of a semigroup of positive quasinilpotent integral operators on
$C({\cal K})$ where ${\cal K}$ is a compact Hausdorff space.
Category:47B65 

104. CMB 1998 (vol 41 pp. 137)
 Choksi, J. R.; Nadkarni, M. G.

Genericity of certain classes of unitary and selfadjoint operators
In a paper [1], published in 1990, in a (somewhat inaccessible)
conference proceedings, the authors had shown that for the unitary
operators on a separable Hilbert space, endowed with the strong
operator topology, those with singular, continuous, simple spectrum,
with full support, form a dense $G_\delta$. A similar theorem for
bounded selfadjoint operators with a given norm bound (omitting
simplicity) was recently given by Barry Simon [2], [3], with a totally
different proof. In this note we show that a slight modification of
our argument, combined with the Cayley transform, gives a proof of
Simon's result, with simplicity of the spectrum added.
Category:47B15 

105. CMB 1998 (vol 41 pp. 240)
 Xia, Jingbo

On certain $K$groups associated with minimal flows
It is known that the Toeplitz algebra associated with any flow
which is both minimal and uniquely ergodic always has a trivial
$K_1$group. We show in this note that if the unique ergodicity is
dropped, then such $K_1$group can be nontrivial. Therefore, in
the general setting of minimal flows, even the $K$theoretical
index is not sufficient for the classification of Toeplitz
operators which are invertible modulo the commutator ideal.
Categories:46L80, 47B35, 47C15 

106. 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 

107. CMB 1998 (vol 41 pp. 129)
108. CMB 1998 (vol 41 pp. 49)
 Harrison, K. J.; Ward, J. A.; Eaton, LJ.

Stability of weighted darma filters
We study the stability of linear filters associated with certain types of
linear difference equations with variable coefficients. We show that
stability is determined by the locations of the poles of a rational transfer
function relative to the spectrum of an associated weighted shift operator.
The known theory for filters associated with constantcoefficient difference
equations is a special case.
Keywords:Difference equations, adaptive $\DARMA$ filters, weighted shifts,, stability and boundedness, automatic continuity Categories:47A62, 47B37, 93D25, 42A85, 47N70 

109. CMB 1998 (vol 41 pp. 10)
 Borwein, David

Simple conditions for matrices to be bounded operators on $l_p$
The two theorems proved yield simple yet reasonably
general conditions for triangular matrices to be bounded
operators on $l_p$. The theorems are applied to N\"orlund and
weighted mean matrices.
Keywords:Triangular matrices, NÃ¶rlund matrices, weighted means, operators, on $l_p$. Categories:47B37, 47A30, 40G05 

110. CMB 1997 (vol 40 pp. 443)
111. CMB 1997 (vol 40 pp. 464)
 Kuo, ChungCheng

On the solvability of a Neumann boundary value problem at resonance
We study the existence of solutions of the semilinear equations (1)
$\triangle u + g(x,u)=h$, ${\partial u \over \partial n} = 0$ on
$\partial \Omega$ in which the nonlinearity $g$ may grow
superlinearly in $u$ in one of directions $u \to \infty$ and $u \to
\infty$, and (2) $\triangle u + g(x,u)=h$, ${\partial u \over
\partial n} = 0$ on $\partial \Omega$ in which the nonlinear term $g$
may grow superlinearly in $u$ as $u \to \infty$. The purpose of this
paper is to obtain solvability theorems for (1) and (2) when the
LandesmanLazer condition does not hold. More precisely, we require
that $h$ may satisfy $\int g^\delta_ (x) \, dx < \int h(x) \, dx = 0<
\int g^\gamma_+ (x)\,dx$, where $\gamma, \delta$ are arbitrarily
nonnegative constants, $g^\gamma_+ (x) = \lim_{u \to \infty} \inf
g(x,u) u^\gamma$ and $g^\delta_ (x)=\lim_{u \to \infty} \sup
g(x,u)u^\delta$. The proofs are based upon degree theoretic arguments.
Keywords:LandesmanLazer condition, Leray Schauder degree Categories:35J65, 47H11, 47H15 

112. CMB 1997 (vol 40 pp. 193)