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1.
In this paper we first show that if X is a Banach space and is a left invariant crossnorm on lX, then there is a Banach lattice L and an isometric embedding J of X into L, so that I J becomes an isometry of lX onto lm J(X). Here I denotes the identity operator on l and lm J(X) the canonical lattice tensor product. This result is originally due to G. Pisier (unpublished), but our proof is different. We then use this to prove the main results which characterize the Gordon–Lewis property GL and related structures in terms of embeddings into Banach lattices. 相似文献
2.
Siegfried Steiner 《manuscripta mathematica》1977,20(3):277-300
Let E be a n-dimensional euclidean vector space. The subset V
k
n
={x ... x | x E} of kE is called a Veronesemanifold. The scalar product of E induces a euclidean structure on kE. Passing to the corresponding projective space
, one may consider
as a riemannian submanifold of the space form
. In this paper we study properties of the pair
of riemannian manifolds. 相似文献
3.
R. Zekri 《K-Theory》1990,3(6):543-559
We show that the universalC*-algebras KqA and K2A are homotopy equivalent and define abstract analogues of the Bott elements inKK-theory. 相似文献
4.
The long-known results of Schreier on group extensions are here raised to a categorical level by giving a factor set theory for torsors under a categorical group (G,) over a small category . We show a natural bijection between the set of equivalence classes of such torsors and [B({}),B(G,)], the set of homotopy classes of continuous maps between the corresponding classifying spaces. These results are applied to algebraically interpret the set of homotopy classes of maps from a CW-complex X to a path-connected CW-complex Y with
i
(Y)=0 for all i1,2. 相似文献
5.
Micheline Vigué-Poirrier 《manuscripta mathematica》1986,56(2):177-191
Let X be a nilpotent space such that it exists k1 with Hp (X,) = 0 p > k and Hk (X,) 0, let Y be a (m–1)-connected space with mk+2, then the rational homotopy Lie algebra of YX (resp.
is isomorphic as Lie algebra, to H* (X,) (* (Y) ) (resp.+ (X,) (* (Y) )). If X is formal and Y -formal, then the spaces YX and
are -formal. Furthermore, if dim * (Y) is infinite and dim H* (Y,Q) is finite, then the sequence of Betti numbers of
grows exponentially. 相似文献
6.
Normality preserving multiplication operators 总被引:1,自引:0,他引:1
We show that a multiplication operator (T)=ATB is normality preserving if and only if it is hyponormality preserving, if and only if it is either of the formA=fg,B=h f, orA=D,B=D* for someC andD* D=I. Also we show that is (semi-) Fredholmness prserving if and only ifA andB are (semi-) Fredholm operators.Supported by the Science Foundation of Zhejiang Province and NSF. 相似文献
7.
The non-commutative torus C
*(n,) is realized as the C*-algebra of sections of a locally trivial C*-algebra bundle over S with fibres isomorphic to C
*n/S, 1) for a totally skew multiplier 1 on n/S. D. Poguntke [9] proved that A
is stably isomorphic to C(S) C(*( Zn/S, 1) C(S) A Mkl( C) for a simple non-commutative torus A and an integer kl. It is well-known that a stable isomorphism of two separable C*-algebras is equivalent to the existence of equivalence bimodule between them. We construct an A-C(S) A-equivalence bimodule. 相似文献
8.
Andrew Ranicki 《K-Theory》1987,1(2):115-170
The algebraic K-theory product K
0(A) K
1
B K
1(A B) for rings A, B is given a chain complex interpretation, using the absolute torsion invariant introduced in Part I. Given a finitely dominated A-module chain complex C and a round finite B-module chain complex D, it is shown that the A B-module chain complex C D has a round finite chain homotopy structure. Thus, if X is a finitely dominated CW complex and Y is a round finite CW complex, the product X × Y is a CW complex with a round finite homotopy structure. 相似文献
9.
N. R. Rocco 《Bulletin of the Brazilian Mathematical Society》1991,22(1):63-79
LetG andG
be isomorphic groups. We introduce and study a quotient (G) of the free productG *G
which is a group extention of the non-abelian tensor squareG G. This seems to bring computational advantages to calculate this last group. Looking over as an operator in the class of groups we prove that it preserves properties of the argumentG such as finiteness, set of prime divisors, nilpotency and solvability. For a finitep-groupG we find a good polynomial bound for the order of (G). 相似文献
10.
Emmanuel Germain 《K-Theory》2001,23(1):41-52
We consider for unital c
*-algebras the short exact sequence 0 I A *
C
B A max B 0and give an explicit formula for the boundary map for separable C
*-algebras for which the Künneth formula for tensor products holds without Tor-terms. In the course of the article, we study the similar case of an ideal concerning one-relator groups. 相似文献
11.
In this article the topologically exact sequences
of locally convex spaces are characterized for which for every locally convex space F the map id : FE F Q is a homomorphism, or equivalently, the map id L : FK F E is a topological injection. This is motivated by the problem of lifting Q-valued functions with certain given properties to E-valued functions with the same or slightly weaker properties, which may also be considered as the investigation of parameter dependences of solutions of linear (differential) equations. Applications to partial differential equations and to Fredholm functions are given. 相似文献
12.
Toshiyuki Kobayashi 《Inventiones Mathematicae》1994,117(1):181-205
Summary LetGG be real reductive Lie groups and q a -stable parabolic subalgebra of Lie (G) . This paper offers a sufficient condition on (G, G, q) that the irreducible unitary representation
ofG with non-zero continuous cohomology splits into a discrete sum of irreducible unitary representations of a subgroupG, each of finite multiplicity. As an application to purely analytic problems, new results on discrete series are also obtained for some pseudo-Riemannian (non-symmetric) spherical homogeneous spaces, which fit nicely into this framework. Some explicit examples of a decomposition formula are also found in the cases whereA
q is not necessarily a highest weight module.Oblatum 3-IV-1993The author is supported by the NSF grant DMS-9100383. 相似文献
13.
Zusammenfassung Gegeben seien endliche MengenX, Y undZ X × Y, Z
x
={y¦(x,y) Z},Z
y
={x¦(x,y) Z}.Man nenntA X (bzw.B Y)zuordenbar, wenn es eine Injektion:A Y (bzw.: B X) mit(x) Z
x
(bzw.(y) Z
y
) gibt, und (A, B) mit #A=#B > 0 einZuordnungspaar, wenn eine Bijektionf:A B mitf(x)Z
x
B (bzw.f
–1
(y) Z
y
A) existiert. Die Bijektionf heißtZuordnungsplan fürA, B.In der vorliegenden Arbeit werden Fragen nach der Existenz von optimal zuordenbaren Mengen und optimalen Zuordnungspaaren behandelt, wenn man auf den MengenX undY Ordnungen vorgibt, wobei auch Nebenbedingungen berücksichtigt werden. In manchen Fällen lassen sich anhand der Beweise Zuordnungspläne oder ihre Berechnungsvorschrift explizit angeben.Zum Schluß werden die Aussagen an konkreten, dem Bereich der Wirtschaftswissenschaften entnommenen Beispielen erläutert.
Diese Arbeit ist mit Unterstützung des Sonderforschungsbereiches 72 an der Universität Bonn entstanden. 相似文献
Summary LetX, Y be finite sets andZ X × Y, Z x ={y¦(x,y) Z},Z y ={x¦(x,y)Z}. A X (resp.B Y) is calledassignable if there is an injection: A Y (resp.: B X) with (x) Z x (resp.(y) Z y ), (A, B) with #A=#B > 0 anassigned pair if there is a bijection f:A B withf (x) Z x B (resp.f –1(y) Z y A). The bijectionf is called aplan forA andB.In this paper problems are discussed concerning the existence of optimal assignable sets and optimal assigned pairs ifX andY are totally ordered, additional constraints are also considered. In some cases the proofs give explicit constructions of plans. The results are illustrated by application to problems occurring in Operations Research.
Diese Arbeit ist mit Unterstützung des Sonderforschungsbereiches 72 an der Universität Bonn entstanden. 相似文献
14.
LetA be a von Neumann algebra and a faithful normal state. ThenO
= {
ºAd(g
1) :g G
A
}andU
= {
ºAd(u
*) :u U
A
are homogeneous reductive spaces. IfA is aC
* algebra,e
the Jones projection of the faithful state viewed as a conditional expectation, then we prove that the similarity orbit ofe
by invertible elements ofA can be imbedded inAA in such a way thate
is carried to 1 1 and the orbit ofe
to a homogeneous reductive space and an analytic submanifold ofAA. 相似文献
15.
Rangachari Venkataraman 《Monatshefte für Mathematik》1985,100(1):47-66
An abelian topological group is an group if and only if it is a locally -compactk-space and every compact subset in it is contained in a compactly generated locally compact subgroup. Every abelian groupG is topologically isomorphic to G
0 where 0 andG
0 is an abelian group where every compact subset is contained in a compact subgroup. Intrinsic definitions of measures, convolution of measures, measure algebra,L
1-algebra, Fourier transforms of abelian groups are given and their properties are studied. 相似文献
16.
M. Guyot 《Mathematische Annalen》1985,270(1):47-62
Conclusion SoitE un fibré uniforme surG(d,n). Nous avons étudié exhaustivement les cas où rangEd. montrant queE est soit somme directe de fibrés ou droites, soit, sir=d, indécomposable et isomorphe àH
d
O
G
() où àH
d
*
O
G
().Si rangE=(n-d), nous avons étudié les cas oùE est décomposable en fibrés en droites ou indécomposable et isomorphe àQ
n d
O
G
() où àQ
n
*
d
O
G
(). L'étude des fibrés indécomposables de rangd, et (n-d) nous a montré que les quatre fibrés universels surG(d,n), sont caractérisés par leur rang, leur polynôme de Chern et al propriété d'uniformité. 相似文献
17.
P. Gabriel L. A. Nazarova A. V. Roiter V. V. Sergeichuk D. Vossieck 《Ukrainian Mathematical Journal》1993,45(3):335-372
Assume thatB is a finite-dimensional algebra over an algebraically closed fieldk, B
d
=Spec k[(B
d
] is the affine algebraic scheme whoseR-points are theB k k[Bd]-module structures onR
d, and Md is a canonical Bk k[Bd]-module supported by k[Bd]d. Further, say that an affine subscheme of Bd isclass true if the functor Fgn X Md k[B] X induces an injection between the sets of isomorphism classes of indecomposable finite-dimensional modules over k[] andB. If Bd contains a class-true plane for somed, then the schemes Be contain class-true subschemes of arbitrary dimensions. Otherwise, each Bd contains a finite number of classtrue puncture straight linesL(d, i) such that for eachn, almost each indecomposableB-module of dimensionn is isomorphic to someF
L(d, i) (X); furthermore,F
L(d, i) (X) is not isomorphic toF
L(l, j) (Y) if(d, i) (l, j) andX 0. The proof uses a reduction to subspace problems, for which an inductive algorithm permits us to prove corresponding statements.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 3, pp. 313–352, March, 1993. 相似文献
18.
Summary The notion of a quantum Poisson process over a quantum measure space is introduced. This process is used to construct new quantum Markov processes on the matrix algebraM
n
with stationary faithful state . If (, ) is the quantum measure space in question ( a von Neumann algebra and a faithful normal weight), then the semigroupe
tL
of transition operators on (M
n
, ) has generator whereu is an arbitrary unitary element of the centraliser of (M
n
,).Supported by the Netherlands Organization for Scientific Research NWO 相似文献
19.
V. N. Sudakov 《Mathematical Notes》1973,14(4):886-888
Let X and Y be locally compact-compact topological spaces, F X×Y is closed, and P(F) is the set of all Borel probability measures on F. For us to find, for the pair of probability measures (x, y P (X)×P(Y), a probability measure P(F) such that
X
=
X
–1
,
Y
=
Y
–1
it is necessary and sufficient that, for any pair of Borel sets A X, B Y for which (A× B) F=Ø, the condition
XA+
YB 1 holds.Translated from Matematicheskie Zametki, Vol. 14, No. 4, pp. 573–576, October, 1973. 相似文献
20.
Let H be the extended Cuntz algebra over the Hilbert space H. Since its zero grade part H0 is the C*-inductive limit of B(Hr), we look for some family of representations on an inductive limit of Hr as r. When such construction is shaped according to the structure of H0, von Neumanns notion of a reference sequence of unit vectors for Hilbert infinite tensor products emerges; after a further Rieffel induction step, a class IPR[H] of representations of H arises. For any two such representations, we describe explicitly their associated intertwiners. Any two representations in IPR[H] are either disjoint or unitarily equivalent. Actions of the group by translation on sequences of unit vectors are involved, as well as the ideals of . 相似文献