共查询到20条相似文献,搜索用时 109 毫秒
1.
Andreas Blass 《Archive for Mathematical Logic》1990,30(1):1-11
We prove several theorems about the cardinal
associated with groupwise density. With respect to a natural ordering of families of nond-ecreasing maps from to, all families of size
are below all unbounded families. With respect to a natural ordering of filters on, all filters generated by
sets are below all non-feeble filters. If
then
and
. (The definitions of these cardinals are recalled in the introduction.) Finally, some consequences deduced from
by Laflamme are shown to be equivalent to
. 相似文献
2.
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
3.
Prof. Ottmar Loos 《Monatshefte für Mathematik》1978,86(2):107-129
Every Jordan pair
defines an algebraic varietyX containing
as a dense open subset.X is projective (affine) if and only if
is separable (radical). The Picard group ofX is generated by the irreducible factors of the generic norm of
. If
is separable then the automorphism group ofX is the projective group of
. 相似文献
4.
5.
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
6.
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
7.
LetF be an algebraic number field and F such thatx
m– is irreducible, wherem is an integer. Let
be a prime ideal inF with
. The prime decomposition of
in
is explicitly obtained in the following cases. Case 1:
, (a,m) = 1 (where
means
, 0
). Case 2:m lt, wherel is a prime andl 0
. Case 3:m 0
and every prime that dividesm also dividespf–1. It is not assumed that thev
th roots of unity are inF for anyv 2. 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.
Aparna W. Higgins 《Algebra Universalis》1985,20(2):179-193
Given a group G and a descending chainG
0,G
1,...,G
n, of normal subgroups ofG, we prove that there exists a universal algebra
, such that the chain ...Wn(
)...W1(
}) W0(
)W(
) is isomorphic to the chain ...G
n ...G
1G
0G, where W(
) is the group of weak automorphisms of
, and Wn(
) is the group of weak automorphisms of
that leaves alln-ary operations fixed.We also prove that there are an infinite number of non-isomorphic algebras that satisfy the above.These results are a generalization of those proved by J. Sichler, in the special case when G=G0, and G1=G2=...=Gn=....Presented by J. Mycielski.This paper comprises part of the author's doctoral dissertation at the University of Notre Dame in 1983. The author wishes to express her deep gratitude to Professor Abraham Goetz for suggesting this problem, for being extremely generous with his time and experience, and for giving her his constant encouragement. The author also thanks the reviewer for his helpful comments. 相似文献
10.
Ralph McKenzie 《Algebra Universalis》1984,18(1):29-69
A construction is defined which associates, to every algebra
of a fixed but arbitrary finite similarity type, a groupoidF
. The identities ofF
are finitely based if and only if those of
are, andF
is finite if and only if
is finite. Up to isomorphism,F
has the same endomorphism monoid and subalgebra lattice as
, but the congruence lattice ofF
is the result of adjoining a new 1 to the congruence lattice of
.F is functorial, preserves the satisfaction (and the non-satisfaction) of most Mal'cev conditions, and produces, by composition with the operation of forming the generated variety, an isomorphism of the lattice of varieties of fixed type to an interval in the lattice of varieties of groupoids.The construction makes use of a new product operation, applicable to two algebras of differing similarity types, which is introduced and studied in this paper.Research supported by National Science Foundation grant MCS-8103455.Presented by K. A. Baker. 相似文献
11.
Let (,G, U) be a continuous representation of a Lie groupG by bounded operatorsg U (g) on the Banach space and let (,
,dU) denote the representation of the Lie algebra
obtained by differentiation. Ifa
1, ...,a
d
is a Lie algebra basis of
,A
i
=dU (a
i
) and
whenever =(i
1, ...,i
k
) we reconsider the operators
相似文献
12.
The class
of orthomodular lattices which have only finitely many commutators is investigated. The following theorems are proved:
contains the block-finite orthomodular lattices. Every irreducible element of
is simple. Every element of
is a direct product of a Boolean algebra and finitely many simple orthomodular lattices. The irreducible elements of
which are modular, or are M-symmetric with at least one atom, have height two or less. 相似文献
13.
M. Emery 《Probability Theory and Related Fields》1980,51(1):95-100
Summary Let (,
, P) be a complete probability space; let
t0 be an increasing right-continuous family of
-complete sub--fields of
; let
be a sequence of semimartingales. Assume that for all positive t and for all bounded predictable processes H, the r.v.'s
converge in probability to a limit J(t, H) when n tends to infinity. Then there exists a semimartingale X such that, for all t and H, J(t, H)=
. 相似文献
14.
Brendan Mc Cann 《Annali di Matematica Pura ed Applicata》1990,157(1):27-61
Summary
We present a Fitting Class construction which exploits the properties of a certain class of finite soluble groups of nilpotent length three, called
-groups in the paper. In addition we look at a wider class of groups, called
in the paper, also of nilpotent length three and examine the question as to what
-groups are in
.A number of examples are given to illuminate the various classes.The author would like to thank HermannHeineken for supervising his dissertation, from which this paper has sprung, the German Academic Exchange Service (DAAD) for enabling him to study with Prof. Heineken at Universität Würzburg and An Roinn Oideachais for the fellowship which is at present supporting him at University College, Galway. 相似文献
15.
D. I. Panyushev 《Functional Analysis and Its Applications》2004,38(1):38-44
Let
be a reductive Lie algebra over an algebraically closed field of characteristic zero and
an arbitrary
-grading. We consider the variety
, which is called the commuting variety associated with the
-grading. Earlier it was proved by the author that
is irreducible, if the
-grading is of maximal rank. Now we show that
is irreducible for
and (E6,F4). In the case of symmetric pairs of rank one, we show that the number of irreducible components of
is equal to that of nonzero non--regular nilpotent G
0-orbits in
. We also discuss a general problem of the irreducibility of commuting varieties. 相似文献
16.
In this paper we investigate functorial properties of the Segal algebra
which consists of all functionsf in Wiener's algebra onG with Fourier transform
in Wiener's algebra on the dual group
. Especially
may serve as a very large and natural domain for Poisson's formula. Moreover, there is introduced a Segal algebraE
0(G) containing
as a subspace, but still eachfE
0(S) satisfies Poisson's formula. 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.
Lutz Strüngmann 《Israel Journal of Mathematics》2006,151(1):29-51
LetR be a unital associative ring and
two classes of leftR-modules. In [St3] the notion of a (
) pair was introduced. In analogy to classical cotorsion pairs, a pair (V,W) of subclasses
is called a (
) pair if it is maximal with respect to the classes
and the condition Ext
R
1
(V, W)=0 for all
. In this paper we study
pairs whereR = ℤ and
is the class of all torsion-free abelian groups andT is the class of all torsion abelian groups. A complete characterization is obtained assumingV=L. For example, it is shown that every
pair is singly cognerated underV=L.
The author was supported by a DFG grant. 相似文献
19.
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
20.
V. Yu. Popov 《Algebra and Logic》2001,40(1):55-66
It is proved that there exists an infinite sequence of finitely based semigroup varieties
such that, for all i, an equational theory for
and for the class
of all finite semigroups in
is undecidable while an equational theory for
and for the class
of all finite semigroups in
is decidable. An infinite sequence of finitely based semigroup varieties
is constructed so that, for all i, an equational theory for
and for the class
of all finite semigroups in
is decidable whicle an equational theory for
and for the class
of all finite semigroups in
is not. 相似文献
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