Expand all Collapse all | Results 401 - 419 of 419 |
401. CMB 1999 (vol 42 pp. 139)
Essential Norm and Weak Compactness of Composition Operators on Weighted Banach Spaces of Analytic Functions |
Essential Norm and Weak Compactness of Composition Operators on Weighted Banach Spaces of Analytic Functions Every weakly compact composition operator between weighted Banach
spaces $H_v^{\infty}$ of analytic functions with weighted sup-norms is
compact. Lower and upper estimates of the essential norm of
continuous composition operators are obtained. The norms of the point
evaluation functionals on the Banach space $H_v^{\infty}$ are also
estimated, thus permitting to get new characterizations of compact
composition operators between these spaces.
Keywords:weighted Banach spaces of holomorphic functions, composition operator, compact operator, weakly compact operator Categories:47B38, 30D55, 46E15 |
402. CMB 1999 (vol 42 pp. 13)
Dow's Principle and $Q$-Sets A $Q$-set is a set of reals every subset of which is a relative
$G_\delta$. We investigate the combinatorics of $Q$-sets and
discuss a question of Miller and Zhou on the size $\qq$ of the smallest
set of reals which is not a $Q$-set. We show in particular that various
natural lower bounds for $\qq$ are consistently strictly smaller than
$\qq$.
Keywords:$Q$-set, cardinal invariants of the continuum, pseudointersection number, $\MA$($\sigma$-centered), Dow's principle, almost disjoint family, almost disjointness principle, iterated forcing Categories:03E05, 03E35, 54A35 |
403. CMB 1999 (vol 42 pp. 125)
Modular Vector Invariants of Cyclic Permutation Representations Vector invariants of finite groups (see the introduction for an
explanation of the terminology) have often been used to illustrate the
difficulties of invariant theory in the modular case: see,
\eg., \cite{Ber}, \cite{norway}, \cite{fossum}, \cite{MmeB},
\cite{poly} and \cite{survey}. It is therefore all the more
surprising that the {\it unpleasant} properties of these invariants
may be derived from two unexpected, and remarkable, {\it nice}
properties: namely for vector permutation invariants of the cyclic
group $\mathbb{Z}/p$ of prime order in characteristic $p$ the
image of the transfer homomorphism $\Tr^{\mathbb{Z}/p} \colon
\mathbb{F}[V] \lra \mathbb{F}[V]^{\mathbb{Z}/p}$ is a prime ideal,
and the quotient algebra $\mathbb{F}[V]^{\mathbb{Z}/p}/ \Im
(\Tr^{\mathbb{Z}/p})$ is a polynomial algebra on the top Chern
classes of the action.
Keywords:polynomial invariants of finite groups Category:13A50 |
404. CMB 1999 (vol 42 pp. 118)
Points of Weak$^\ast$-Norm Continuity in the Unit Ball of the Space $\WC(K,X)^\ast$ For a compact Hausdorff space with a dense set of isolated points, we
give a complete description of points of weak$^\ast$-norm continuity
in the dual unit ball of the space of Banach space valued functions
that are continuous when the range has the weak topology. As an
application we give a complete description of points of weak-norm
continuity of the unit ball of the space of vector measures when
the underlying Banach space has the Radon-Nikodym property.
Keywords:Points of weak$^\ast$-norm continuity, space of vector valued weakly continuous functions, $M$-ideals Categories:46B20, 46E40 |
405. CMB 1999 (vol 42 pp. 104)
InstabilitÃ© de vecteurs propres d'opÃ©rateurs linÃ©aires We consider some geometric properties of eigenvectors of linear
operators on infinite dimensional Hilbert space. It is proved that
the property of a family of vectors $(x_n)$ to be eigenvectors
$Tx_n= \lambda_n x_n$ ($\lambda_n \noteq \lambda_k$ for $n\noteq k$)
of a bounded operator $T$ (admissibility property) is very instable
with respect to additive and linear perturbations. For instance,
(1)~for the sequence $(x_n+\epsilon_n v_n)_{n\geq k(\epsilon)}$ to
be admissible for every admissible $(x_n)$ and for a suitable
choice of small numbers $\epsilon_n\noteq 0$ it is necessary and
sufficient that the perturbation sequence be eventually scalar:
there exist $\gamma_n\in \C$ such that $v_n= \gamma_n v_{k}$ for
$n\geq k$ (Theorem~2); (2)~for a bounded operator $A$ to transform
admissible families $(x_n)$ into admissible families $(Ax_n)$ it is
necessary and sufficient that $A$ be left invertible (Theorem~4).
Keywords:eigenvectors, minimal families, reproducing kernels Categories:47A10, 46B15 |
406. CMB 1999 (vol 42 pp. 97)
On Analytic Functions of Bergman $\BMO$ in the Ball Let $B = B_n$ be the open unit ball of $\bbd C^n$ with
volume measure $\nu$, $U = B_1$ and ${\cal B}$ be the Bloch space on
$U$. ${\cal A}^{2, \alpha} (B)$, $1 \leq \alpha < \infty$, is defined
as the set of holomorphic $f\colon B \rightarrow \bbd C$ for which
$$
\int_B \vert f(z) \vert^2 \left( \frac 1{\vert z\vert}
\log \frac 1{1 - \vert z\vert } \right)^{-\alpha}
\frac {d\nu (z)}{1-\vert z\vert} < \infty
$$
if $0 < \alpha <\infty$ and ${\cal A}^{2, 1} (B) = H^2(B)$, the Hardy
space. Our objective of this note is to characterize, in terms of
the Bergman distance, those holomorphic $f\colon B \rightarrow U$ for
which the composition operator $C_f \colon {\cal B} \rightarrow
{\cal A}^{2, \alpha}(B)$ defined by $C_f (g) = g\circ f$,
$g \in {\cal B}$, is bounded. Our result has a corollary that
characterize the set of analytic functions of bounded mean
oscillation with respect to the Bergman metric.
Keywords:Bergman distance, \BMOA$, Hardy space, Bloch function Category:32A37 |
407. CMB 1998 (vol 41 pp. 497)
On the construction of HÃ¶lder and Proximal Subderivatives We construct Lipschitz functions such that for all $s>0$ they are
$s$-H\"older, and so proximally, subdifferentiable only on dyadic
rationals and nowhere else. As applications we construct Lipschitz
functions with prescribed H\"older and approximate subderivatives.
Keywords:Lipschitz functions, HÃ¶lder subdifferential, proximal subdifferential, approximate subdifferential, symmetric subdifferential, HÃ¶lder smooth, dyadic rationals Categories:49J52, 26A16, 26A24 |
408. CMB 1998 (vol 41 pp. 348)
Characterizing continua by disconnection properties We study Hausdorff continua in which every set of certain
cardinality contains a subset which disconnects the space. We show
that such continua are rim-finite. We give characterizations of
this class among metric continua. As an application of our
methods, we show that continua in which each countably infinite set
disconnects are generalized graphs. This extends a result of
Nadler for metric continua.
Keywords:disconnection properties, rim-finite continua, graphs Categories:54D05, 54F20, 54F50 |
409. CMB 1998 (vol 41 pp. 267)
On the nonemptiness of the adjoint linear system of polarized manifold Let $(X,L)$ be a polarized manifold over the complex number field
with $\dim X=n$. In this paper, we consider a conjecture of
M.~C.~Beltrametti and A.~J.~Sommese and we obtain that this
conjecture is true if $n=3$ and $h^{0}(L)\geq 2$, or $\dim \Bs
|L|\leq 0$ for any $n\geq 3$. Moreover we can generalize the
result of Sommese.
Keywords:Polarized manifold, adjoint bundle Categories:14C20, 14J99 |
410. CMB 1998 (vol 41 pp. 207)
An oscillation criterion for first order linear delay differential equations A new oscillation criterion is given for the delay differential
equation $x'(t)+p(t)x \left(t-\tau(t)\right)=0$, where $p$, $\tau
\in \C \left([0,\infty),[0,\infty)\right)$ and the function
$T$ defined by $T(t)=t-\tau(t)$, $t\ge 0$ is increasing and such
that $\lim_{t\to\infty}T(t)=\infty$. This criterion concerns the
case where $\liminf_{t\to\infty} \int_{T(t)}^{t}p(s)\,ds\le
\frac{1}{e}$.
Keywords:Delay differential equation, oscillation Category:34K15 |
411. 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 |
412. CMB 1998 (vol 41 pp. 41)
On the Clarke subdifferential of an integral functional on $L_p$, $1\leq p < \infty$ Given an integral functional defined on $L_p$, $1 \leq p <\infty$,
under a growth condition we give an upper bound of the Clarke
directional derivative and we obtain a nice inclusion between the
Clarke subdifferential of the integral functional and the set of
selections of the subdifferential of the integrand.
Keywords:Integral functional, integrand, epi-derivative Categories:28A25, 49J52, 46E30 |
413. CMB 1998 (vol 41 pp. 71)
Splitting patterns and trace forms The splitting pattern of a quadratic form $q$ over
a field $k$ consists of all distinct Witt indices that occur for $q$
over extension fields of $k$. In small dimensions, the complete list
of splitting patterns of quadratic forms is known. We show that
{\it all\/} splitting patterns of quadratic forms of dimension at
most nine can be realized by trace forms.
Keywords:Quadratic forms, Witt indices, generic splitting. Category:11E04 |
414. 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 |
415. CMB 1997 (vol 40 pp. 488)
CaractÃ©risations spectrales du radical et du socle d'une paire de jordan-banach If $f$ and $g$ are two analytic functions from a domain $D$ of the
complex plane into respectively the Banach spaces $V^+$ and $V^-$,
we prove that $\lambda\mapsto \Sp\bigl(f(\lambda),g(\lambda)\bigr)$ is an
analytic multivalued function. From this derives the subharmonicity of the
functions $\lambda\mapsto \rho_V\bigl(f(\lambda),g(\lambda)\bigr)$
and $\lambda\mapsto \log\rho_V\bigl(f(\lambda),g(\lambda)\bigr)$ where
$\rho$ denotes the spectral radius. We apply these results to obtain nice
caracterizations of the radical and the socle of a Banach Jordan pair,
and finally we get an algebraic structural theorem.
Keywords:Spectre, rayon spectral, multifonction analytique, quasi-inverse,, paire de Jordan-Banach, radical de Jacobson, socle. Categories:46H70, (17A15) |
416. CMB 1997 (vol 40 pp. 169)
The class $A^{+}_{\infty}(\lowercase{g})$ and the one-sided reverse HÃ¶lder inequality We give a direct proof that $w$ is an $A^{+}_{\infty}(g)$ weight if and only
if $w$ satisfies a one-sided, weighted reverse H\"older inequality.
Keywords:one-sided maximal operator, one-sided $(A_\infty)$, one-sided, reverse HÃ¶lder inequality Category:42B25 |
417. CMB 1997 (vol 40 pp. 54)
A note on $U_n\times U_m$ modular invariants We consider the rings of invariants $R^G$, where $R$ is the symmetric
algebra of a tensor product between two vector spaces over the field $F_p$
and $G=U_n\times U_m$. A polynomial algebra is constructed and these
invariants provide Chern classes for the modular cohomology of $U_{n+m}$.
Keywords:Invariant theory, cohomology of the unipotent group Category:13F20 |
418. CMB 1997 (vol 40 pp. 60)
Cauchy's problem for harmonic functions with entire data on a sphere We give an elementary potential-theoretic proof of a theorem of
G.~Johnsson: all solutions of Cauchy's problems for the Laplace
equations with an entire data on a sphere extend harmonically to
the whole space ${\bf R}^N$ except, perhaps, for the center of the
sphere.
Keywords:harmonic functions, Cauchy's problem, homogeneous harmonics Categories:35B60, 31B20 |
419. CMB 1997 (vol 40 pp. 47)
A universal coefficient decomposition for subgroups induced by submodules of group algebras Dimension subgroups and Lie dimension subgroups are known to satisfy a
`universal coefficient decomposition', {\it i.e.} their value with respect to
an arbitrary coefficient ring can be described in terms of their values with
respect to the `universal' coefficient rings given by the cyclic groups of
infinite and prime power order. Here this fact is generalized to much more
general types of induced subgroups, notably covering Fox subgroups and
relative dimension subgroups with respect to group algebra filtrations
induced by arbitrary $N$-series, as well as certain common generalisations
of these which occur in the study of the former. This result relies on an
extension of the principal universal coefficient decomposition theorem on
polynomial ideals (due to Passi, Parmenter and Seghal), to all additive
subgroups of group rings. This is possible by using homological instead
of ring theoretical methods.
Keywords:induced subgroups, group algebras, Fox subgroups, relative dimension, subgroups, polynomial ideals Categories:20C07, 16A27 |