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1.
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
2.
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
3.
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
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.
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
6.
A study is undertaken of order-reversing maps on series-parallel posets and structural characterisations are obtained of various subclasses of such ordered sets. The results are applied to complete the authors' earlier investigation of classes
of finite relate
lattices, where
is a variety of Ockham lattices and the distributive lattice duals of the algebras in
are required to be series-parallel. 相似文献
7.
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
8.
D. N. Dudin 《Mathematical Notes》1968,3(1):42-44
For an algebra
of subsets of a set X there is constructed a set
and an algebra of its subsets so that the mapping
is a one-to-one correspondence between
and
and for each additive measure on
the measure
on
defined by the equation
is countably additive.Translated from Matematicheskie Zametki, Vol. 3, No. 1, pp. 71–76, January, 1968.The author wishes to express his deep appreciation to S. V. Fomin, under whose guidance this paper was written. 相似文献
9.
We show three main results concerning Hamiltonicity of graphs derived from antimatroids. These results provide Gray codes for the feasible sets and basic words of antimatroids.For antimatroid (E,
), letJ(
) denote the graph whose vertices are the sets of
, where two vertices are adjacent if the corresponding sets differ by one element. DefineJ(
;k) to be the subgraph ofJ(
)2 induced by the sets in
with exactlyk elements. Both graphsJ(
) andJ(
;k) are connected, and the former is bipartite.We show that there is a Hamiltonian cycle inJ(
)×K
2. As a consequence, the ideals of any poset % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgznf% gDOfdaryqr1ngBPrginfgDObYtUvgaiuaacqWFpepuaaa!414C!\[\mathcal{P}\] may be listed in such a way that successive ideals differ by at most two elements. We also show thatJ(
;k) has a Hamilton path if (E,
) is the poset antimatroid of a series-parallel poset.Similarly, we show thatG(
)×K
2 is Hamiltonian, whereG(
) is the basic word graph of a language antimatroid (E,
). This result was known previously for poset antimatroids.Research supported in part by NSERC.Research supported in part by the Natural Sciences and Engineering Research Council of Canada under Grant A3379. 相似文献
10.
We introduce the notion ofweak subnormality, which generalizes subnormality in the sense that for the extension
ofT
we only require that
hold forf
; in this case we call
a partially normal extension ofT. After establishing some basic results about weak subnormality (including those dealing with the notion of minimal partially normal extension), we proceed to characterize weak subnormality for weighted shifts and to prove that 2-hyponormal weighted shifts are weakly subnormal. Let {
n
}
n=0
be a weight sequence and letW
denote the associated unilateral weighted shift on
. IfW
is 2-hyponormal thenW
is weakly subnormal. Moreover, there exists a partially normal extension
on
such that (i)
is hyponormal; (ii)
; and (iii)
. In particular, if is strictly increasing then
can be obtained as
whereW
is a weighted shift whose weight sequence {
n
·
n=0
is given by
In this case,
is a minimal partially normal extension ofW
. In addition, ifW
is 3-hyponormal then
can be chosen to be weakly subnormal. This allows us to shed new light on Stampfli's geometric construction of the minimal normal extension of a subnormal weighted shift. Our methods also yield two additional results: (i) the square of a weakly subnormal operator whose minimal partially normal extension is always hyponormal, and (ii) a 2-hyponormal operator with rank-one self-commutator is necessarily subnormal. Finally, we investigate the connections of weak subnormality and 2-hyponormality with Agler's model theory.Supported by NSF research grant DMS-9800931.Supported by the Brain Korea 21 Project from the Korean Ministry of Education. 相似文献
11.
We deal with the Kreîn-Langer problem for
-valued functions on the band (–2a, 2a)×, where
is the algebra of continuous linear operators on a Hilbert space
,a a finite positive number and a topological Abelian group. We show that every weakly continuous -indefinite function
admits a strongly continuous -indefinite continuation to × with the same indefiniteness index . We give a parametrization of the extensions in terms of operator-valued Schur functions. 相似文献
12.
Ignacio Bajo 《Monatshefte für Mathematik》1994,118(1-2):1-6
Let
be a complex Lie algebra,
its underlying real Lie algebra,
a real form of
and ·, · the euclidean product induced by the real part of an hermitian inner product on
. Let aut
be the Lie algebra of skew-symmetric derivations of
. We give necessary and sufficient conditions to ensure that aut
is composed of skew-hermitian derivations. As an application, we study holomorphy in large subgroups of isometries of Lie groups. 相似文献
13.
Daoxing Xia 《Integral Equations and Operator Theory》1999,33(4):489-506
This paper studies the class of pure operatorsA on a Hilbert space
satisfying dimK
A
<, where
. The main tool is a pair of matrices
and
. A reproducing kernel Hilbert space model is introduced for a subclass of this class of operators. Some theorems are established for some subnormal operators as well as hyponormal operators in this class. 相似文献
14.
The strongly irreducible operators in nest algebras 总被引:2,自引:0,他引:2
An operatorT on
is called strongly irreducible ifT does not commute with any nontrivial idempotent operator. In this paper, we first show that each nest algebra (
) has strongly irreducible operators. Secondly, we obtain a characterization of operators which can be uniquely written as a direct sum of finitely many strongly irreducible operators. Finally, we characterize the strongly irreducibility of operators in a nest algebra (
).This project was partially supported by National Natural Science Foundation of China. 相似文献
15.
In 1997, V. Pták defined the notion of generalized Hankel operator as follows: Given two contractions
and
, an operatorX:
is said to be a generalized Hankel operator ifT
2
X=XT
1
*
andX satisfies a boundedness condition that depends on the unitary parts of the minimal isometric dilations ofT
1 andT
2. The purpose behind this kind of generalization is to study which properties of classical Hankel operators depend on their characteristic intertwining relation rather than on the theory of analytic functions. Following this spirit, we give appropriate versions of a number of results about compact and finite rank Hankel operators that hold within Pták's generalized framework. Namely, we extend Adamyan, Arov and Krein's estimates of the essential norm of a Hankel operator, Hartman's characterization of compact Hankel operators and Kronecker's characterization of finite rank Hankel operators.Dedicated to the memory of our master and friend Vlastimil Pták 相似文献
16.
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
17.
William M. McGovern 《Inventiones Mathematicae》1989,97(1):209-217
Summary LetG be a complex semisimple algebraic group with Lie algebra
. Let
be a nilpotentG-orbit,
its ring of regular functions. We derive a formula for
as aG-module and prove some partial results on
a cover of
. We then relate this formula to various existing multiplicity formulas forK-types in Harish-Chandra bimodules ofG.Supported by National Science Foundation Grant DMS-8505550 相似文献
18.
Mohan Namasivayam 《Annali di Matematica Pura ed Applicata》1986,144(1):157-172
Summary
Integral representations of junctions in the anisotropic Sobolev spaces
on unbounded domains are used in the study of the embeddings of these spaces into Lebesgue spaces. Estimates of entropy numbers of the embedding
are obtained, where k, p and q satisfy certain conditions and where is a certain type of quasibounded domain, 相似文献
19.
Gerd Herzog 《Periodica Mathematica Hungarica》1995,30(3):205-210
Given a sequence (
n
)
n
in
with
there are functions
such that
, is a dense subset of
, and the set of functions with this property is residual in
. We will show that in
and some related Banach spaceX there are functionsf with
is dense in
, and we will give a sufficient condition when the set of such functions is residual inX. 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