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1.
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
2.
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
3.
Summary Let
denote the extended Weyl algebra,
, the Weyl algebra. It is well known that every element of
of the formA=B
k
*
B
k
is positive. We prove that the converse implication also holds: Every positive elementA in
has a quadratic sum factorization for some finite set of elements (B
k
) in
. The corresponding result is not true for the subalgebra
. We identify states on
which do not extend to states on
. It follows from a result of Powers (and Arveson) that such states on
cannot be completely positive. Our theorem is based on a certain regularity property for the representations which are generated by states on
, and this property is not in general shared by representations generated by states defined only on the subalgebra
.Work supported in part by the NSF 相似文献
4.
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
5.
S. N. Chernikov 《Mathematical Notes》1968,4(1):543-545
It is proved that if a periodic group
has an extremal normal divisor
, determining a complete abelian factor group
, then the center of the group
contains a complete abelian subgroup
, satisfying the relation
and intersecting
on a finite subgroup. It is also established with the aid of this proposition that every periodic group of automorphisms of an extremal group
is a finite extension of a contained in it subgroup of inner automorphisms of the group
.Translated from Matematicheskie Zametki, Vol. 4, No. 1, pp. 91–96, July, 1968. 相似文献
6.
Let
denote the closed subspace of
consisting of analytic functions in the unit disk
. For certain class of subharmonic
, the Hankel operatorH
b on
with symbol
is studied. Criteria for boundedness and compactness of such kind of Hankel operators are presented.R. Rochberg's research was partially supported by a grant from the National Science Foundation. 相似文献
7.
S. Yu. Orevkov 《Mathematical Notes》2000,68(5-6):588-593
Dehornoy constructed a right invariant order on the braid group B
n uniquely defined by the condition
1{\text{ if }}\beta _0 ,\beta _1$$
" align="middle" border="0">
are words in
. A braid is called strongly positive if
1$$
" align="middle" border="0">
for any
. In the present paper it is proved that the braid
is strongly positive if the word
does not contain
. We also provide a geometric proof of the result by Burckel and Laver that the standard generators of a braid group are strongly positive. Finally, we discuss relations between the right invariant order and quasipositivity. 相似文献
8.
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
9.
Dr. Detlev Poguntke 《Monatshefte für Mathematik》1976,82(1):31-50
This is a continuation of the paper Zwei Klassen lokalkompakter maximal fastperiodischer Gruppen, [6]. In [6], the classes
and
were introduced. We give sufficient conditions to conclude thatG is in
if one knows thatG/G
0 is in
. If a groupG is in
and ifG satisfies the Chu-duality then all closed subgroups ofG satisfy the Chu-duality. The Chu-quasi-dual of the Heisenberg groupH with integral coefficients is computed. It is shown thatH does not satisfy the Chu-duality, thatH is in
, and thatH is not in
. 相似文献
10.
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
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.
Helmut Schaeffer 《Journal of Geometry》1984,22(1):51-56
Dilatations of a plane K2 (K a field) are mappings such that
and
are linearly dependent vectors for all P,Q K2. In this note we describe mappings of K2 into itself such that
and
are linearly dependent only if P=Q+(z,1/z), z K, z O, by derivations of K. In finite planes we get dilatations as before.
Professor A. Barlotti zum 60. Geburtstag zugeeignet 相似文献
Professor A. Barlotti zum 60. Geburtstag zugeeignet 相似文献
13.
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
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. Schinzel 《Monatshefte für Mathematik》1986,102(4):309-337
Letk>1 and let
be non-zero algebraic numbers contained in the field
. It is shown that for almost all, in the sense of density integer vectorsn
1,...,n
k
the polynomial
becomes irreducible over
on dividing by the product of all factorsx–, where is a root of unity.Dedicated to Professor E. Hlawka on the occasion of his seventieth birthday 相似文献
16.
Oswald Riemenschneider 《manuscripta mathematica》1974,14(1):91-99
Let
be a 1-convex holomorphic mapping between complex spaces
resp.S, and let
be the blowingdown factorization of
over S. We prove in part 1 of the present note: The fiber –1(s0) over a point s0S is the Remmert quotient of
if and only if every holomorphic function on
(defined in a neighborhood of the exceptional subvariety of that fiber) can be extended holomorphically to
. This is true, for instance, in the case:
flat, S reduced at s0 and dim
, =const for all sS. In part 2, we use this result to obtain the following: For any Riemann surface R with genus g2 there exists a 2-dimensional normal complex analytic singularity X such that the minimal resolution
of X contains R as exceptional subvariety, and
has a deformation over the unit disc S={|s|<1} which can not be blown down to a deformation of X. 相似文献
17.
A linear operatorT L(H) is called a strongly irreducible, if there is no non-trivial idempotent linear operator commuting withT. In this paper, denote the set of all strongly irreducible operators by (SI). Let
be a nest with infinite dimensional atoms,
be the nest algebra associated with
and
be the closure of
, then the following result is proved
.The projection partially supported by Chinese Natural Science Foundation and Fund of Laboratory of Nonlinear Mathematical Modeling and Methods in Fudan University in Shanghai P.R.C. 相似文献
18.
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
19.
Hans Werner Schuster 《manuscripta mathematica》1969,1(2):125-137
This article deals with deformations of compact complex spaces, the parameter-space being a general complex space. A compact space X0 is called absolutely rigid, if every deformation of X0 is trivial. Ex(X0,
) is defined as the group of the extensions of
by
and it is shown that X0 is absolutely rigid if and only if Ex(X0,
)=0.If X0 is reduced, there is Ex(X0,
). The proof makes use of the results of M.A{uprtin} [1] and D{upouady} [2]. 相似文献
20.
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