Expand all Collapse all | Results 76 - 88 of 88 |
76. CMB 1999 (vol 42 pp. 87)
Some norm inequalities for operators Let $A_i$, $B_i$ and $X_i$ $(i=1, 2, \dots, n)$ be operators on a
separable Hilbert space. It is shown that if $f$ and $g$ are
nonnegative continuous functions on $[0,\infty)$ which satisfy the
relation $f(t)g(t) =t$ for all $t$ in $[0,\infty)$, then
$$
\Biglvert \,\Bigl|\sum^n_{i=1} A^*_i X_i B_i \Bigr|^r \,\Bigrvert^2
\leq \Biglvert \Bigl( \sum^n_{i=1} A^*_i f (|X^*_i|)^2 A_i \Bigr)^r
\Bigrvert \, \Biglvert \Bigl( \sum^n_{i=1} B^*_i g (|X_i|)^2 B_i
\Bigr)^r \Bigrvert
$$
for every $r>0$ and for every unitarily invariant norm. This result
improves some known Cauchy-Schwarz type inequalities. Norm
inequalities related to the arithmetic-geometric mean inequality and
the classical Heinz inequalities are also obtained.
Keywords:Unitarily invariant norm, positive operator, arithmetic-geometric mean inequality, Cauchy-Schwarz inequality, Heinz inequality Categories:47A30, 47B10, 47B15, 47B20 |
77. CMB 1998 (vol 41 pp. 413)
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 |
78. CMB 1998 (vol 41 pp. 434)
Linear maps on factors which preserve the extreme points of the unit ball The aim of this paper is to characterize those linear maps from a
von~Neumann factor $\A$ into itself which preserve the extreme points
of the unit ball of $\A$. For example, we show that if $\A$ is infinite,
then every such linear preserver can be written as a fixed unitary
operator times either a unital $\ast$-homomorphism or a unital
$\ast$-antihomomorphism.
Categories:47B49, 47D25 |
79. CMB 1998 (vol 41 pp. 298)
On the ideal-triangularizability of semigroups of quasinilpotent positive operators on $C({\cal K})$ |
On the ideal-triangularizability 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 Hausdorff-Lindel\"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 ideal-triangularizability
of a semigroup of positive quasinilpotent integral operators on
$C({\cal K})$ where ${\cal K}$ is a compact Hausdorff space.
Category:47B65 |
80. CMB 1998 (vol 41 pp. 137)
Genericity of certain classes of unitary and self-adjoint 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 self-adjoint 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 |
81. CMB 1998 (vol 41 pp. 240)
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 non-trivial. 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 |
82. CMB 1998 (vol 41 pp. 196)
Brown-Halmos 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 Brown-Halmos type and
Hartman-Wintner type are studied.
Keywords:Toeplitz operator, singular integral, operator, weighted Hardy space, spectrum. Category:47B35 |
83. CMB 1998 (vol 41 pp. 129)
Pluriharmonic symbols of commuting Toeplitz type operators on the weighted Bergman spaces A class of Toeplitz type operators acting on the
weighted Bergman spaces of the unit ball in the $n$-dimensional complex
space is considered and two pluriharmonic symbols of commuting
Toeplitz type operators are completely characterized.
Keywords:Pluriharmonic functions, Weighted Bergman spaces, Toeplitz type operators. Categories:47B38, 32A37 |
84. CMB 1998 (vol 41 pp. 49)
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 constant-coefficient 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 |
85. CMB 1998 (vol 41 pp. 10)
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 |
86. CMB 1997 (vol 40 pp. 443)
Reflective Representations and Banach C*-Modules Suppose ${\cal A}$ is a unital $C$*-algebra and $m\colon{\cal A}\to B(X)$
Categories:47D30, 46L99 |
87. CMB 1997 (vol 40 pp. 464)
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 non-linearity $g$ 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
Landesman-Lazer 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:Landesman-Lazer condition, Leray Schauder degree Categories:35J65, 47H11, 47H15 |
88. CMB 1997 (vol 40 pp. 193)
Finite rank operators and functional calculus on Hilbert modules over abelian $C^{\ast}$-algebras We consider the problem: If $K$ is a compact normal operator on a Hilbert
module $E$, and $f\in C_0(\Sp K)$ is a function which is zero in a
neighbourhood of the origin, is $f(K)$ of finite rank? We show that
this is the case if the underlying $C^{\ast}$-algebra is abelian, and that
the range of $f(K)$ is contained in a finitely generated projective
submodule of $E$.
Categories:55R50, 47A60, 47B38 |