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1.
In this paper, we consider equations of the form
, where
is a function with values in the Hilbert space
, the operator B is symmetric, and the operator A is uniformly positive and self-adjoint in
. The linear operator
generating the C
0-semigroup in the energy space
is associated with this equation. We prove that this semigroup is exponentially stable if the operator B is uniformly positive and the operator A dominates B in the sense of quadratic forms. 相似文献
2.
Roman Drnovšek 《Integral Equations and Operator Theory》2001,39(3):253-266
Let
be a collection of bounded operators on a Banach spaceX of dimension at least two. We say that
is finitely quasinilpotent at a vectorx
0X whenever for any finite subset
of
the joint spectral radius of
atx
0 is equal 0. If such collection
contains a non-zero compact operator, then
and its commutant
have a common non-trivial invariant, subspace. If in addition,
is a collection of positive operators on a Banach lattice, then
has a common non-trivial closed ideal. This result and a recent remarkable theorem of Turovskii imply the following extension of the famous result of de Pagter to semigroups. Let
be a multiplicative semigroup of quasinilpotent compact positive operators on a Banach lattice of dimension at least two. Then
has a common non-trivial invariant closed ideal.This work was supported by the Research Ministry of Slovenia. 相似文献
3.
Let
and
be adjoint nilpotent orbits in a real semisimple Lie algebra. Write
≥
if
is contained in the closure of
. This defines a partial order on the set of such orbits, known as the closure ordering. We determine this order for the split
real form of the simple complex Lie algebra, E
8. The proof is based on the fact that the Kostant-Sekiguchi correspondence preserves the closure ordering. We also present
a comprehensive list of simple representatives of these orbits, and list the irreeducible components of the boundaries
and of the intersections
. 相似文献
4.
Takuya Hara 《Integral Equations and Operator Theory》1992,15(4):551-567
Let
be a Hilbert space. A continuous positive operatorT on
uniquely determines a Hilbert space
which is continuously imbedded in
and for which
with the canonical imbedding
. A Kreîn space version of this result, however, is not valid in general. This paper provides a necessary and sufficient condition for that a continuous selfadjoint operatorT uniquely determines a Kreîn space (
) which is continuously imbedded in
and for which
with the canonical imbedding
. 相似文献
5.
We prove that if a group G is residually
, then for every
-subgroup of the group G, the set of -roots from this subgroup is a -separable
-subgroup. 相似文献
6.
Let
be an
-filtered category in the sense of Karoubi. This is the categorical analogue of an ideal
in a ring
. Pedersen and Weibel constructed a fibration of K-theory spectra associated with the sequence
. We present a new easier proof based on Waldhausen' generic fibration. 相似文献
7.
FUBINITHEOREMw.r.t.STOCHASTICMEASUREONPRODUCTMEASURABLESPACECHENPEIDE(陈培德)(InstituteofAppliedMathematics,theChineseAcademyofS... 相似文献
8.
Graeme West 《Integral Equations and Operator Theory》1995,22(3):352-359
Suppose
is a von Neumann algebra on a Hilbert space
and
is any ideal in
. We determine a topology
on
, for which the members of
that are
to norm continuous are exactly those in
; and a bornology
on
such that the elements of
which map the unit ball to an element of
, equivalently those members of
that are norm to
bounded, are exactly those in
. This is achieved via analogues of the notions of injectivity and surjectivity in the theory of operator ideals on Banach spaces. 相似文献
9.
Avishay Vaknin 《K-Theory》2001,24(1):57-68
For a small triangulated category
, Bass's K
1 group
is described, and the theorem of the heart is proved. We define the determinant map from
to Neeman's
, and we compute this map when
is the derived category of an Abelian category
. 相似文献
10.
G. L. Booth 《Periodica Mathematica Hungarica》1991,22(3):175-182
The Brown-McCoy radical
is known to be an ideal-hereditary Kurosh-Amitsur radical in the variety of zerosymmetric near-rings. We define the Brown-McCoy and simplical radicals,
and
, respectively, for zerosymmetric -near-rings. Both
and
are ideal-hereditary Kurosh-Amitsur radicals in that variety. IfM is a zerosymmetric -near-ring with left operator near-ringL, it is shown that
, with equality ifM has a strong left unity.
is extended to the variety of arbitrary near-rings, and
and
are extended to the variety of arbitrary -near-rings, in a way that they remain Kurosh-Amitsur radicals. IfN is a near-ring andA N, then
, with equality ifA if left invariant. 相似文献
11.
Let (G,
) denote a finite groupG with fibration
. The group Aut (G,
) of operators of (G,
) is closely related to the group of collineations of (G,
). In this paper we investigate the geometric properties imposed on (G,
) by requiring that Aut (G,
)=AutG. We find that in many instances this algebraic property restricts the geometry to a very special form.Dedicated to Professor Helmut Karzel on the occasion of his 60th birthday. 相似文献
12.
El-B. Yallaoui 《Periodica Mathematica Hungarica》1991,23(2):109-120
Let X be an abstract set and L a lattice of subsets of X. To each lattice regular measure µ, we associate two induced measures
and
on suitable lattices of the Wallman space IR(L) and another measure µ on the spaceIR(L). We will investigate the reflection of smoothness properties of p onto
,
and µ; and try to set some new criterion for repleteness and measure repleteness. 相似文献
13.
Marilyn Breen 《Geometriae Dedicata》1996,60(3):283-288
Let
be a family of simple polygons in the plane. If every three (not necessarily distinct) members of
have a simply connected union and every two members of
have a nonempty intersection, then {P:P in
}
. Applying the result to a finite family
of orthogonally convex polygons, the set {C:C in
} will be another orthogonally convex polygon, and, in certain circumstances, the dimension of this intersection can be determined.Supported in part by NSF grant DMS-9207019. 相似文献
14.
N. L. Vasilevski 《Integral Equations and Operator Theory》1999,34(1):107-126
Let
be the unit disk in,
be the Bergman space, consisting of all analytic functions from
, and
be the Bergman projection of
onto
. We constructC
*-algebras
, for functions of which the commutator of Toeplitz operators [T
a
,T
b
]=T
a
T
b
–T
b
T
a
is compact, and, at the same time, the semi-commutator [T
a
,T
b
)=T
a
T
b
–T
ab
is not compact.It is proved, that for each finite set =n
0,n
1, ...,n
m
, where 1=n
0
1
<...
m
, andn
k
{}, there are algebras
of the above type, such that the symbol algebras Sym
of Toeplitz operator algebras
arecommutative, while the symbol algebras Sym
of the algebras
, generated by multiplication operators
and
, haveirreducible representations exactly of dimensions n
0,n
1,..., n
m
.This work was partially supported by CONACYT Project 3114P-E9607, México. 相似文献
15.
Edgar R. Lorch 《Integral Equations and Operator Theory》1981,4(3):422-434
The objects studied are the subalgebras of
which contain co. These are isometrically isomorphic to the algebras C(
) where
is a compactification of a discrete denumerable set N . It is shown: 1) If
is metric then there is a projection of norm 1, P: C(
) C(
) with kernel co defined by PF = f o where is a retraction of
onto
=
– N . 2) If
is metric, then the group of homeomorphisms of
is isomorphic to a complete group of permutations of the natural numbers . 3) The group of homeomorphisms of a compact metric space is the homomorphic image of a complete group of permutations of ("complete" means "no outer automorphisms, trivial center"). 相似文献
16.
LetT be a contraction acting in a separable Hilbert space
and leaving invariant a nest
of subspaces of
. We answer the question: when doesT have an isometric extension to
which leaves invariant the nest
= {N N :N
;}. 相似文献
17.
Palle E. T. Jorgensen 《Integral Equations and Operator Theory》1999,35(2):125-171
This paper is devoted to an approximation problem for operators in Hilbert space, that appears when one tries to study geometrically thecascade algorithm in wavelet theory. Let
be a Hilbert space, and let be a representation ofL
(
) on
. LetR be a positive operator inL
(
) such thatR(1) =1, where1 denotes the constant function 1. We study operatorsM on
(bounded, but noncontractive) such that
where the * refers to Hilbert space adjoint. We give a complete orthogonal expansion of
which reduces such thatM acts as a shift on one part, and the residual part is
() =
n
[M
n
], where [M
n
] is the closure of the range ofM
n
. The shift part is present, we show, if and only if ker (M
*){0}. We apply the operator-theoretic results to the refinement operator (or cascade algorithm) from wavelet theory. Using the representation , we show that, for this wavelet operatorM, the components in the decomposition are unitarily, and canonically, equivalent to spacesL
2(E
n
) L
2(), whereE
n , n=1,2,3,..., , are measurable subsets which form a tiling of ; i.e., the union is up to zero measure, and pairwise intersections of differentE
n
's have measure zero. We prove two results on the convergence of the cascale algorithm, and identify singular vectors for the starting point of the algorithm.Terminology used in the paper
the one-torus
-
Haar measure on the torus
-
Z
the Zak transform
-
X=ZXZ
–1
transformation of operators
-
a given Hilbert space
-
a representation ofL
(
) on
-
R
the Ruelle operator onL
(
)
-
M
an operator on
-
R
*,M
*
adjoint operators
Work supported in part by the U.S. National Science Foundation. 相似文献
18.
Mikael R?rdam 《K-Theory》1995,9(1):31-58
A classification is given of the simple Cuntz-Krieger algebras
. It is proved that these algebras are classified up to stable isomorphism by their K0-group. Thus the sign of the determinant of 1 —A is not an isomorphism invariant. The (non-stabilized) isomorphism type of
is determined by K0(
) together with the position of the class of the unit of
. 相似文献
19.
吴启光 《应用数学学报(英文版)》1995,11(4):378-388
QUADRATICESTIMATORSOFQUADRATICFUNCTIONSWITHPARAMETERSINNORMALLINEARMODELS¥WUQIGUANG(吴启光)(InstituteofSystemeScience,theChinese... 相似文献
20.
Let
and
the foliations by the null geodesics of some lorentzian metricg on the torus
. We analyse how geodesic completeness properties ofg are related to the dynamics of
and
. 相似文献