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1.
We study the boundedness and compactness of commutators
on
, where
and
are defined by
and
respectively. If
satisfies some upper and lower estimates, then we obtain a necessary and sufficient condition
for
to be bounded or compact on
for
.
The reproducing kernel of the harmonic Bergman space of
can be shown
to satisfy all the required estimates. Our result is the real variable analogue
of the complex variable one for commutators associated with an analytic reproducing
kernel. 相似文献
2.
Estimates of Marcinkiewicz Integrals with Bounded Homogeneous Kernels of Degree Zero 总被引:2,自引:0,他引:2
Under the cancellation property and a certain Dini-type condition
on kernels, we prove that Marcinkiewicz integrals with kernels which are homogeneous
functions of degree zero, are bounded from
to
,
from
to
, and from
to
for
. 相似文献
3.
The C*-algebra
generated by the Bergman and anti-Bergman projections and by the operators of multiplication by piecewise continuous functions on the Lebesgue space L2(Π) over the upper half-plane is studied. Making use of a local principle, limit operators techniques, and the Plamenevsky results on two-dimensional singular integral operators with coefficients admitting homogeneous discontinuities we reduce the study to simpler C*-algebras associated with points
and pairs
We construct a symbol calculus for unital C*-algebras generated by n orthogonal projections sum of which equals the unit and by m one-dimensional orthogonal projections. Such algebras are models of local algebras at points z ∈∂Π being the discontinuity points of coefficients. A symbol calculus for the C*- algebra
and a Fredholm criterion for the operators
are obtained. Finally, a C*-algebra isomorphism between the quotient algebra
where
is the ideal of compact operators, and its analogue
for the unit disk is constructed. 相似文献
5.
An Operator Transform from Class A to the Class of Hyponormal Operators and its Application 总被引:1,自引:0,他引:1
In this paper, we shall give an operator transform
from class A to the class of hyponormal operators. Then we shall show that
and
in case T belongs to class A. Next, as an application of
we will show that every class A operator has SVEP and property (β). 相似文献
6.
We consider the three-dimensional Schrödinger operators
and
where
, A is a magnetic potential generating a constant magnetic
field of strength
, and
where
decays fast enough at infinity. Then, A. Pushnitskis representation of the spectral shift function (SSF)
for the pair of operators
is well defined for energies
We study the behaviour of the associated representative of the equivalence class
determined by the SSF, in a neighbourhood of the Landau levels
Reducing our analysis to the study of the eigenvalue asymptotics for a family of
compact operators of Toeplitz type, we establish a relation between the type of the
singularities of the SSF at the Landau levels and the decay rate of V at infinity.
Communicated by Bernard HelfferSubmitted 23/09/03, accepted 15/01/04 相似文献
7.
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
8.
9.
In this note we give an example of an ∞-hyponormal operator T whose Aluthge transform
is not (1+ɛ)-hyponormal for any ɛ > 0 and show that the sequence
of interated Aluthge transforms of T need not converge in the weak operator topology, which solve two problems in [6]. 相似文献
10.
The aim of this paper is to prove two perturbation results for a selfadjoint operator A in a Krein space
which can roughly be described as follows: (1) If is an open subset of
and all spectral subspaces for A corresponding to compact subsets of have finite rank of negativity, the same is true for a selfadjoint operator B in
for which the difference of the resolvents of A and B is compact. (2) The property that there exists some neighbourhood of such that the restriction of A to a spectral subspace for A corresponding to is a nonnegative operator in
is preserved under relative
perturbations in form sense if the resulting operator is again selfadjoint. The assertion (1) is proved for selfadjoint relations A and B. (1) and (2) generalize some known results. 相似文献
11.
Let B(H) denote the algebra of operators on a complex Hilbert
space H, and let U denote the class of operators
which satisfy
the absolute value condition
.
It is proved that if
is a
contraction, then either A has a nontrivial invariant subspace or A is a proper
contraction and the nonnegative operator
is strongly stable. A Putnam-Fuglede type commutativity theorem is proved for contractions A in
,
and it is shown that if normal subspaces of
. It is proved that if
are reducing, then every compact operator in the intersection of the weak closure of the range of the
derivation
with the commutant of A* is quasinilpotent. 相似文献
12.
We investigate the ideal structure of the Toeplitz algebra
of a totally ordered abelian group
. We show that the primitive ideals of
are parametrised by the disjoint union
of the duals
of the order ideals
of
, and identify the
hull-kernel topology on
when the chain of orderideals in
is isomorphic to a subset of
相似文献
13.
Summary.
We study certain functional equations derived from the
definition of a Jordan *-derivation pair.
More precisely, if A is a complex
*-algebra and M is a
bimodule over A, having the structure of a complex vector space
compatible with the structure of A,
such that
implies
m = 0 and
implies m
= 0 and
if
are unknown additive mappings satisfying
then E and
F can be represented by double centralizers. The
obtained result implies that one of the equations in the
definition of a Jordan *-derivation pair is redundant.
Furthermore, a remark on the extension of this result to unknown
additive mappings
such that
is given in a special case. 相似文献
14.
The goal of this paper is to extend some previous results on abelian ideals of Borel subalgebras to so-called spherical ideals of
These are ideals
of
such that their G-saturation
is a spherical G-variety. We classify all maximal spherical ideals of
for all simple G.Received: 25 March 2004 相似文献
15.
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
16.
Let S be a real interval with
, and
be a function satisfying
We show that if h is Lebesgue or Baire measurable, then there
exists
such that
That result is motivated by a question of E. Manstaviius.
Received: 11 February 2003 相似文献
17.
Let G be a finite group,
a normal subgroup, p a prime,
a finite splitting field of characteristic p for
G and
We prove that
is a splitting field for N, using the action
of the Galois group of the field extension
on the irreducible representations of N.
As
is a splitting field for the symmetric group
Sn
we get as a corollary that
is a splitting field for the alternating group
An.
Received: 31 July 2003 相似文献
18.
The shadow minimization problem for t-intersecting systems of finite sets is considered. Let
be a family of k-subsets of . The -shadow of
is the set of all (k-)-subsets
contained in the members of
. Let
be a t-intersecting family (any two members have at least t elements in common) with
. Given k,t,m the problem is to minimize
(over all choices of
). In this paper we solve this problem when m is big enough. 相似文献
19.
Let T be an M-hyponormal operator acting on infinite dimensional separable Hilbert space and let
be the Riesz idempotent for λ0, where D is a closed disk of center λ0 which contains no other points of σ (T). In this note we show that E is self-adjoint and
As an application, if T is an algebraically M-hyponormal operator then we prove : (i) Weyl’s theorem holds for f(T) for every
(ii) a-Browder’s theorem holds for f(S) for every
and f ∈ H(σ(S)); (iii) the the spectral mapping theorem holds for the Weyl spectrum of T and for the essential approximate point spectrum of T. 相似文献
20.
Alejandra Maestripieri Francisco Martínez Pería 《Integral Equations and Operator Theory》2007,59(2):207-221
The aim of this work is to generalize the notions of Schur complements and shorted operators to Krein spaces. Given a (bounded)
J-selfadjoint operator A (with the unique factorization property) acting on a Krein space
and a suitable closed subspace
of
, the Schur complement
of A to
is defined. The basic properties of
are developed and different characterizations are given, most of them resembling those of the shorted of (bounded) positive
operators on a Hilbert space.
To the memory of Professor Mischa Cotlar 相似文献