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1.
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
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.
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
4.
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
5.
Xingde Dai 《Integral Equations and Operator Theory》1997,27(3):294-313
Let be a nest in a separably acting factor
. We present conditions for a factor
to be a bimodule of the nest subalgebraalgß in
which is singly generated in the norm topology. Some relevant results about the compact ideal
, the quasitriangular algebra and the Calkin algebra are established.This work was supported, in part, by funds provided by the University of North Carolina at Charlotte. 相似文献
6.
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
7.
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
8.
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
9.
By removing the components of at-spread
of a finite projective spacePG(d, q) from each hyperplane ofPG(d, q), the blocks of a regular group divisible design
are obtained We characterize geometrict-spreads as thoset-spreads
which are such that the dual of
is also a group divisible design. 相似文献
10.
Scott McCullough 《Integral Equations and Operator Theory》2001,39(3):335-362
Let
denote an annulus,E a finite subset of
with at least three elements, and
the ideal of functions in
which vanish at the points ofE. The quotient
does not have a completely isometric representation on a finite dimensional Hilbert space. This complements a result of [11] which implies that the quotient has an isometric representation on a Hilbert space of dimension twice the cardinality ofE. 相似文献
11.
A characterization of the complexity of a homogeneous space
of a reductive groupG is given in terms of the mutual position of the tangent Lie algebra of the stabilizer of a generic point of
and the (–1)-eigenspace of a Weyl involution of
.Supported by Russian Foundation for Basic Research, Grant No. 98-01-00598.Supported by the U. S. Civilian Research and Development Foundation, Award No. 206, and Russian Foundation for Basic Research, Grant No. 98-01-00598. 相似文献
12.
Let
be aC-lattice which is strong join principally generated. In this paper, we consider prime elements of
for which every semiprimary element is primary. We show, for example, that a compact nonmaximal primep with this property is principal. We also show that if every primepm has this property, then
is either a one dimensional domain or a primary lattice. It follows that if every primep satisfies the property, and if there are only a finite number of minimal primes in
, then
is the finite direct product of one-dimensional domains and primary lattices. 相似文献
13.
We introduce the notion of hyper-self-duality for Bose-Mesner algebras as a strengthening of formal self-duality. Let
denote a Bose-Mesner algebra on a finite nonempty set X. Fix p X, and let
and
denote respectively the dual Bose-Mesner algebra and the Terwilliger algebra of
with respect to p. By a hyper-duality of
, we mean an automorphism of
such that
for all
; and
is a duality of
.
is said to be hyper-self-dual whenever there exists a hyper-duality of
. We say that
is strongly hyper-self-dual whenever there exists a hyper-duality of
which can be expressed as conjugation by an invertible element of
. We show that Bose-Mesner algebras which support a spin model are strongly hyper-self-dual, and we characterize strong hyper-self-duality via the module structure of the associated Terwilliger algebra. 相似文献
14.
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
15.
A. I. Budkin 《Algebra and Logic》2005,44(4):213-218
Let qG be a quasivariety generated by a group G and
be a non-Abelian quasivariety of groups with a finite lattice of subquasivarieties. Suppose
is contained in a quasivariety generated by the following two groups: a free 2-nilpotent group F2(
2) of rank 2 and a free metabelian (i.e., with an Abelian commutant) group F2(
2) of rank 2. It is proved that either
= qF2(
2) or
= qF2(
2) in this instance.__________Translated from Algebra i Logika, Vol. 44, No. 4, pp. 389–398, July–August, 2005. 相似文献
16.
Günter Mayer 《Numerische Mathematik》1985,46(1):69-83
Summary Let
be a real irreduciblen×n interval matrix. Then a necessary and sufficient condition is given for the sequence
of the powers of an interval matrix
to converge to a matrix
which is not the null matrix. In addition a criterion for
is proved to decide whether the limit matrix
satisfies the condition of symmetry
. 相似文献
17.
Johannes Ueberberg 《Journal of Geometry》1990,37(1-2):171-180
Generalizing a theorem of Beutelspacher and Seeger, we consider line sets
inP=PG(2t + 1,q),t IN, with the following properties: (1) any (t + 1)-dimensional subspace ofP contains at least one line of
, (2) if a pointx ofP is incident with at least two lines of
then the points in the factor geometryP/x which are induced by the lines of
throughx form a blocking set of type (t, 1) inP/x, (3) any line of
is coplanar with at least one further line of
. We will show that the examples of minimal cardinality are exactly the line sets of Baer subspaces ofP. 相似文献
18.
A. I. Budkin 《Algebra and Logic》2000,39(6):363-369
Let
be a class of all groups G for which the normal closure (x)
G
of every element x belongs to a class
.
is a Levi class generated by
. Let
and
0 be classes of finitely generated nilpotent groups and of torsion-free, finitely generated, nilpotent groups, respectively. We prove that
and
, and so
and
. It is shown that quasivarieties
and
are closed under free products, and that each contains at most one maximal proper subquasivariety. It is also proved that
is closed under free products if so is
. 相似文献
19.
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
20.
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