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1.
We investigate R-bounded representations
, where X is a Banach space and G is a lca group. Observing that Ψ induces a (strongly continuous) group homomorphism
, we are then able to analyze certain classical homomorphisms U (e.g. translations in Lp (G)) from the viewpoint of R-boundedness and the theory of scalar-type spectral operators.
Dedicated to the memory of H. H. Schaefer 相似文献
2.
A weighted norm inequality for the Marcinkiewicz integral operator
is proved when belongs to
. We also give the weighted
Lp-boundedness for a class of Marcinkiewicz integral operators with rough
kernels
and
related to the Littlewood-Paley
-function and the
area integral S, respectively. 相似文献
3.
The C
*-algebra
generated by the n poly-Bergman and m antipoly-Bergman projections and by the operators of multiplication by piecewise continuous functions on the Lebesgue space
L
2(Π) over the upper half-plane is studied. Making use of a local principle, limit operators techniques, and the Plamenevsky
results on two-dimensional convolution operators with symbols admitting homogeneous discontinuities we reduce the study to
simpler C
*-algebras associated with points
and pairs
. Applying a symbol calculus for the abstract unital C
*-algebras generated by N orthogonal projections sum of which equals the unit and by M = n + m one-dimensional orthogonal projections and using relations for the Gauss hypergeometric function, we study local algebras
at points
being the discontinuity points of coefficients. A symbol calculus for the C
*-algebra
is constructed and a Fredholm criterion for the operators
is obtained. 相似文献
4.
Given
, a compact abelian group G and a function
, we identify the maximal (i.e. optimal) domain of the convolution
operator
(as an operator from Lp(G) to itself). This is the
largest Banach function space (with order continuous norm) into which Lp(G)
is embedded and to which
has a continuous extension, still with values
in Lp(G). Of course, the optimal domain depends on p and g. Whereas
is compact, this is not always so for the extension of
to its optimal domain.
Several characterizations of precisely when this is the case are presented. 相似文献
5.
Let B(H) denote the algebra of operators on a complex separable
Hilbert space H, and let A $\in$ B(H) have the polar decomposition A = U|A|.
The Aluthge transform
is defined to be the operator
.
We say that A $\in$ B(H) is p-hyponormal,
.
Let
.
Given p-hyponormal
, such that AB is compact, this
note considers the relationship between
denotes an enumeration in decreasing order repeated according
to multiplicity of the eigenvalues of the
compact operator T (respectively,
singular values of the compact operator T).
It is proved that
is bounded above by
and below by
for all j = 1, 2, . . .
and that if also
is normal, then there exists a unitary
U1 such that
for all j = 1, 2, . . .. 相似文献
6.
Let
be a compact Riemannian manifold without boundary. In this paper, we consider the first nonzero eigenvalue of the p-Laplacian
and we prove that the limit of
when
is 2/d(M), where d(M) is the diameter of M. Moreover, if
is an oriented compact hypersurface of the Euclidean space
or
, we prove an upper bound of
in terms of the largest principal curvature κ over M. As applications of these results, we obtain optimal lower bounds of d(M) in terms of the curvature. In particular, we prove that if M is a hypersurface of
then:
.
Mathematics Subject Classifications (2000): 53A07, 53C21. 相似文献
7.
Long Miao 《Bulletin of the Brazilian Mathematical Society》2007,38(4):585-594
Let
be a class of groups. A subgroup H of a group G is called
-s-supplemented in G, if there exists a subgroup K of G such that G = HK and K/K ∩ HG belongs to
where HG is the maximal normal subgroup of G which is contained in H. The main purpose of this paper is to study some subgroups of Fitting subgroup and generalized Fitting subgroup
-s-supplemented and some new criterions of p-nilpotency of finite groups are obtained.
*This research is supported by the grant of NSFC and TianYuan Fund of Mathematics of China (Grant #10626047). 相似文献
8.
Anders Olofsson 《Integral Equations and Operator Theory》2007,58(4):503-549
We study an operator-valued Berezin transform corresponding to certain standard weighted Bergman spaces of square integrable
analytic functions in the unit disc. The study of this operator-valued Berezin transform relates in a natural way to the study
of the class of n-hypercontractions on Hilbert space introduced by Agler. To an n-hypercontraction
we associate a positive
-valued operator measure dω
n, T
supported on the closed unit disc
in a way that generalizes the above notion of operator-valued Berezin transform. This construction of positive operator measures
dω
n, T
gives a natural functional calculus for the class of n-hypercontractions. We revisit also the operator model theory for the class of n-hypercontractions. The new results here concern certain canonical features of the theory. The operator model theory for the
class of n-hypercontractions gives information about the structure of the positive operator measures dω
n, T
. 相似文献
9.
Let X be a Banach space and let
A be a closed linear operator on
X. It is shown that the abstract Cauchy problem
enjoys maximal regularity in weighted
L
p
-spaces with weights
, where
,
if and only if it has the property of maximal
L
p
-regularity.
Moreover, it is also shown that the derivation operator
admits an
-calculus in weighted
L
p
-spaces.
Received: 26 February 2003 相似文献
10.
In 1993, Y. A. Abramovich, C. D. Aliprantis and O. Burkinshaw showed that every continuous operator with modulus on an lp-space (1 ≤ p < ∞) whose modulus commutes with a non-zero positive operator T on lp that is quasinilpotent at a non-zero positive vector x0 has a non-trivial invariant closed subspace. In this paper, it is proved that if
is a collection of continuous operators with moduli on lp that is finitely modulus-quasinilpotent at a non-zero positive vector x
0 then
and its right modulus sub-commutant
have a common non-trivial invariant closed subspace. In particular, all continuous operators with moduli on l
p
whose moduli commute with a non-zero positive operator I on l
p
that is quasinilpotent at a non-zero positive vector x
0 have a common non-trivial invariant closed subspace, so that all positive operators on l
p
which commute with a non-zero positive operator S on l
p
that is quasinilpotent at a non-zero positive vector x
0 have a common non-trivial invariant closed subspace.
This research was supported by the Natural Science Foundation of Hunan Province of P. R. China (04JJ6004), the Foundation
of Education Department of Hunan Province of P. R. China (04C002) and the Natural Science Foundation of P. R. China (10671147).
Received: 4 December 2005 Revised: 19 June 2006 相似文献
11.
Let M be a right R-module,
the class of all M-small modules, and P a projective cover of M in
[M]. We consider the torsion theories
= (
),
= (
), and
= (
) in
[M], where
is the torsion theory generated by
is the torsion theory cogenerated by
, and
is the dual Lambek torsion theory. We study some conditions for
to be cohereditary, stable, or split, and prove that Rej(M,
) = M
=
(=
=
)
=
GenM(P)
.2000 Mathematics Subject Classification: 16S90 相似文献
12.
The N-commutator
is conjecturally a well-defined nontrivial operation on
for x =
(x
1, ... ,
x
n
)
if and only if N =
n
2 +
2n - 2. This is
proved for n = 2 and confirmed by
computer experiments for n < 5.
Under 2- and 5-commutators the algebra of divergence-free
vector fields in two dimensions is an sh-Lie (strong homotopic
Lie) algebra in the sense of Stasheff. Similarly,
W(2) is an
sh-Lie algebra with respect to 2- and 6-commutators. 相似文献
13.
Positive Solutions for Semipositone
<Emphasis Type="Italic">m</Emphasis>-point Boundary-value
Problems 总被引:7,自引:0,他引:7
Abstract
Let ξ
i
∈ (0, 1) with 0 <
ξ1 < ξ2 <
··· < ξ
m−2 < 1,
a
i
, b
i
∈ [0,∞) with
and
. We consider the
m-point boundary-value
problem
where f(x, y) ≥ −M, and M is a positive constant. We show the
existence and multiplicity of positive solutions by applying the
fixed point theorem in cones.
*Supported by the NSFC (10271095).
GG-110-10736-1003, NWNU-KJCXGC-212 and the Foundation of Major
Project of Science and Technology of Chinese Education
Ministry 相似文献
14.
Egor A. Alekhno 《Positivity》2009,13(1):3-20
Let T be a positive operator on a Banach lattice E. Some properties of Weyl essential spectrum σew(T), in particular, the equality , where is the set of all compact operators on E, are established. If r(T) does not belong to Fredholm essential spectrum σef(T), then for every a ≠ 0, where T−1 is a residue of the resolvent R(., T) at r(T). The new conditions for which implies , are derived. The question when the relation holds, where is Lozanovsky’s essential spectrum, will be considered. Lozanovsky’s order essential spectrum is introduced. A number of
auxiliary results are proved. Among them the following generalization of Nikol’sky’s theorem: if T is an operator of index zero, then T = R + K, where R is invertible, K ≥ 0 is of finite rank. Under the natural assumptions (one of them is ) a theorem about the Frobenius normal form is proved: there exist T-invariant bands such that if
, where , then an operator on Di is band irreducible.
相似文献
15.
Yu Can ZHU 《数学学报(英文版)》2007,23(9):1707-1718
In this paper, we introduce the concepts of q-Besselian frame and (p, σ)-near Riesz basis in a Banach space, where a is a finite subset of positive integers and 1/p+1/q = 1 with p 〉 1, q 〉 1, and determine the relations among q-frame, p-Riesz basis, q-Besselian frame and (p, σ)-near Riesz basis in a Banach space. We also give some sufficient and necessary conditions on a q-Besselian frame for a Banach space. In particular, we prove reconstruction formulas for Banach spaces X and X^* that if {xn}n=1^∞ C X is a q-Besselian frame for X, then there exists a p-Besselian frame {y&*}n=1^∞ belong to X^* for X^* such that x = ∑n=1^∞ yn^*(x)xn for all x ∈ X, and x^* =∑n=1^∞ x^*(xn)yn^* for all x^* ∈ X^*. Lastly, we consider the stability of a q-Besselian frame for the Banach space X under perturbation. Some results of J. R. Holub, P. G. Casazza, O. Christensen and others in Hilbert spaces are extended to Banach spaces. 相似文献
16.
Let C be a set of objects in a triangulated compactly generated category
We denote by
the smallest suspended subcategory closed under coproducts which contains C (the smallest cosuspended subcategory closed under products which contains
C). We prove that if C is a set of compacts objects then
is a t-structure in
where TC
I is the dual of C with respect to an injective cogenerator
I in the category Mod
C. Moreover, we show that:
C is a tilting set if and only if
And, this is equivalent to TCI is a cotilting object in
Received: 28 March 2003 相似文献
17.
L. Olsen 《Monatshefte für Mathematik》2005,146(2):143-157
For a probability measure μ on a subset of
, the lower and upper Lq-dimensions of order
are defined by
We study the typical behaviour (in the sense of Baire’s category) of the Lq-dimensions
and
. We prove that a typical measure μ is as irregular as possible: for all q ≥ 1, the lower Lq-dimension
attains the smallest possible value and the upper Lq-dimension
attains the largest possible value. 相似文献
18.
Eberhard MALKOWSKY M. MURSALEEN Suthep SUANTAI 《数学学报(英文版)》2007,23(3):521-532
Let p = (pk)k=0^∞ be a bounded sequence of positive reals, m C N and u be s sequence of nonzero terms. If x = (xk)k=0^∞ is any sequence of complex numbers we write Δ(m)x for the sequence of the m th order differences of x and Δu^(m)X = {x=(x)k=0^∞ uΔ(m)x ∈ X} for any set X of sequences. We determine the α-, β- and γ-duals of the sets Δμ^(m)X for X=co(p),c(p),l∞(p) and characterize some matrix transformations between these spaces Δ^(m)X. 相似文献
19.
Let X, Y be Banach spaces. We say that a set
is uniformly p–summing if the series
is uniformly convergent for
whenever (xn) belongs to
. We consider uniformly summing sets of operators defined on a
-space and prove, in case X does not contain a copy of c0, that
is uniformly summing iff
is, where T (φ x) = (T#φ) x for all
and x∈X. We also characterize the sets
with the property that
is uniformly summing viewed in
.
Received: 1 July 2005 相似文献
20.
We define the reduced minimum modulus
of a nonzero element a in a unital C
*-algebra
by
. We prove that
. Applying this result to
and its closed two side ideal
, we get that dist
,
and
for any
if RR
= 0, where
and
is the quotient homomorphism and
. These results generalize corresponding results in Hilbert spaces. 相似文献