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1.
Suppose π1(E, F) is the space of all absolutely 1-summing operators between two Banach spacesE andF. We show that ifF has a copy of c0, then π1 (E, F) will have a copy of c0, and under some conditions ifE has a copy of ℓ1 then π1 (E, F) would have a complemented copy of ℓ1. 相似文献
2.
Fang Gensun 《中国科学A辑(英文版)》2001,44(9):1126-1131
The main result of this paper asserts that if a function f is in the class Bπ,p, 1 <p < ∞; that is, those p-integrable functions whose Fourier transforms are supported in the interval [ - π, π], then f and its
derivatives f(j) j = 1, 2, …, can be recovered from its sampling sequence{f(k)} via the cardinal interpolating spline of degree m in the metric
ofL
q(ℝ)), 1 <p=q < ∞, or 11 <p=q < ⩽ ∞. 相似文献
3.
Alan Robinson 《Inventiones Mathematicae》2003,152(2):331-348
We prove that the stable homotopy of any Γ-module F is the homology of a bicomplex Ξ(F), in which the (q−1)st row is the two-sided bar construction ℬ(Lie*
q
,Σ
q
,F[q]). This gives a natural homotopical cotangent bicomplex for graded commutative algebras, in a form suitable for use in a
new obstruction theory for classifying E
∞ ring structures on spectra. The E
∞ structure on certain Lubin-Tate spectra is a corollary.
Oblatum 15-X-2001 & 14-X-2002?Published online: 24 February 2003 相似文献
4.
K VISHNU NAMBOOTHIRI 《Proceedings Mathematical Sciences》2011,121(1):1-18
Consider an irreducible, admissible representation π of GL(2,F) whose restriction to GL(2,F) + breaks up as a sum of two irreducible representations π
+ + π
−. If π = r
θ
, the Weil representation of GL(2,F) attached to a character θ of K
* does not factor through the norm map from K to F, then c ? [^(K*)]\chi\in \widehat{K^*} with (c. q-1)| F * =w K/F(\chi . \theta ^{-1})\vert _{ F^{ * }}=\omega _{ {K/F}} occurs in r
θ
+ if and only if e(qc-1,y0)=e([`(q)]c-1,y0)=1\epsilon(\theta\chi^{-1},\psi_0)=\epsilon(\overline \theta\chi^{-1},\psi_0)=1 and in r
θ
− if and only if both the epsilon factors are − 1. But given a conductor n, can we say precisely how many such χ will appear in π? We calculate the number of such characters at each given conductor n in this work. 相似文献
5.
Douglas W. Larmour 《Mathematische Zeitschrift》2006,252(3):459-472
Throughout this paper, we let (D,σ) be a central F -division algebra with involution σ such that Fσ={d ∈ F|σ(d)=d} is a Henselian valued field. By [11], the valuation on Fσ extends uniquely to a valuation on D. We denote this valuation by v. Moreover, we assume that the characteristic of the residue field, , is not 2. If the valuation on F is discrete, then any quadratic form q can be written as q= q1⊥πq2, where π is a uniformizer and qi are unit forms. Springer's Theorem states that q is isotropic if and only if at least one of the residue forms and is isotropic. In this paper we generalize this result to ɛ -Hermitian forms. In Section 4, we use the connection between involutions on algebras and ɛ-Hermitian forms to prove an analog of the Springer Theorem for involutions.
This paper was part of the author's doctoral dissertation at New Mexico State University. The author wishes to thank his advisor
Pat Morandi for his tireless help. 相似文献
6.
Let F n be the free group of rank n, and let Aut+(F n ) be its special automorphism group. For an epimorphism π : F n → G of the free group F n onto a finite group G we call the standard congruence subgroup of Aut+(F n ) associated to G and π. In the case n = 2 we fully describe the abelianization of Γ+(G, π) for finite abelian groups G. Moreover, we show that if G is a finite non-perfect group, then Γ+(G, π) ≤ Aut+(F 2) has infinite abelianization. 相似文献
7.
A. S. Kondratev 《Siberian Mathematical Journal》2007,48(6):1001-1018
We prove that if L is one of the simple groups E
6(q) and 2
E
6(q) and G is some finite group with the same spectrum as L, then the commutant of G/F(G) is isomorphic to L and the quotient G/G′ is a cyclic {2,3}-group.
Original Russian Text Copyright ? 2007 Kondrat’ev A. S.
The author was supported by the Russian Foundation for Basic Research (Grant 04-01-00463) and the RFBR-NSFC (Grant 05-01-39000).
__________
Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 48, No. 6, pp. 1250–1271, November–December, 2007. 相似文献
8.
O. A. Alekseeva A. S. Kondrat’ev 《Proceedings of the Steklov Institute of Mathematics》2009,266(Z1):10-23
It is proved that, if G is a finite group that has the same set of element orders as the simple group D
p
(q), where p is prime, p ≥ 5 and q ∈ {2, 3, 5}, then the commutator group of G/F(G) is isomorphic to D
p
(q), the subgroup F(G) is equal to 1 for q = 5 and to O
q
(G) for q ∈ {2, 3}, F(G) ≤ G′, and |G/G′| ≤ 2. 相似文献
9.
Let F be a non-Archimedean local field whose residue characteristic is odd. In this paper we develop a theory of newforms
forU (1, 1)(F), building on previous work onSL
2(F). This theory is analogous to the results of Casselman forGL
2(F) and Jacquet, Piatetski-Shapiro, and Shalika forGL
n(F). To a representation π ofU(1, 1)(F), we attach an integer c(π) called the conductor of π, which depends only on theL-packet π containing π. A newform is a vector in π which is essentially fixed by a congruence subgroup of level c(π). We show
that our newforms are always test vectors for some standard Whittaker functionals, and, in doing so, we give various explicit
formulae for newforms. 相似文献
10.
Wen Bin Guo 《数学学报(英文版)》2008,24(10):1751-1757
In this paper, we prove the following theorem: Let p be a prime number, P a Sylow psubgroup of a group G and π = π(G) / {p}. If P is seminormal in G, then the following statements hold: 1) G is a p-soluble group and P' ≤ Op(G); 2) lp(G) ≤ 2 and lπ(G) ≤ 2; 3) if a π-Hall subgroup of G is q-supersoluble for some q ∈ π, then G is q-supersoluble. 相似文献
11.
We study relations between Schatten classes and product operator ideals, where one of the factors is the Banach ideal ΠE,2 of (E, 2)‐summing operators, and where E is a Banach sequence space with ?2 ? E. We show that for a large class of 2‐convex symmetric Banach sequence spaces the product ideal ΠE,2 ○ ??aq,s is an extension of the Schatten class ??F with a suitable Lorentz space F. As an application, we obtain that if 2 ≤ p, q < ∞, 1/r = 1/p + 1/q and E is a 2‐convex symmetric space with fundamental function λE(n) ≈? n1/p, then ΠE,2 ○ Πq is an extension of the Schatten class ??r,q (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
12.
Li Fenggao 《高校应用数学学报(英文版)》2003,18(2):223-229
Let AG(n, F
q) be the n-dimensional affine space over F
q, where F
q is a finite field with q elements. Denote by Γ
(m) the graph induced by m-flats of AG(n, F
q). For any two adjacent vertices E and F of
is studied. In particular, sizes of maximal cliques in Γ
(m) are determined and it is shown that Γ
(m) is not edge-regular when m<n−1.
Supported by the National Natural Science Foundation of China (19571024) and Hunan Provincial Department of Education (02C512). 相似文献
13.
We study codeterminants in the q-Schur algebra S
q
(n,r) and prove that the standard ones form a basis of S
q
(n,r), using a quantized version of the Désarménien matrix. We find elements of the form F
S
1λ
E
T
in Lusztig’s modified enveloping algebra of gl(n), which, up to powers of q, map to the basis of standard codeterminants, where F
S
∈U
– and E
T
∈U
+ are explicitly given products of root vectors, depending on Young tableaux S and T. 相似文献
14.
E. I. Bunina 《Journal of Mathematical Sciences》2008,152(2):155-190
It is proved that (elementary) Chevalley groups G
π(Φ,K) and G
π′(Φ′,K′) (or E
π(Φ,K) and E
π′(Φ′,K′)) over infinite fields K and K′ of characteristic different from 2, with weight lattices Λ and Λ′, respectively, are elementarily equivalent if and only
if the root systems Φ and Φ′ are isomorphic, the fields K and K′ are elementarily equivalent, and the lattices Λ and Λ′ coincide.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 8, pp. 29–77, 2006. 相似文献
15.
LetF
q
be a finite field withq elements, whereq is a power of an odd prime. In this paper, we assume that δ=0,1 or 2 and consider a projective spacePG(2ν+δ,F
q
), partitioned into an affine spaceAG(2ν+δ,F
q
) of dimension 2ν+δ and a hyperplaneℋ=PG(2ν+δ−1,F
q
) of dimension 2ν+δ−1 at infinity. The points of the hyperplaneℋ are next partitioned into three subsets. A pair of pointsa andb of the affine space is defined to belong to classi if the line
meets the subseti of ℋ. Finally, we derive a family of three-class association schemes, and compute their parameters.
This project is supported by the National Natural Science Foundation of China (No. 19571024). 相似文献
16.
Palanivel Manoharan 《manuscripta mathematica》2008,125(1):127-137
For a fibre preserving map ϕ: E → E on a fibration (E, π, B), we construct a grading preserving map T(ϕ, π) between H*(E) and H*(B) that generalizes the Lefschetz number. If T(ϕ, π) is an isomorphism between H
0(E) and H
0(B), then π restricts to a surjective local diffeomorphism on each connected component of the fixed point set of ϕ under a transversality condition. This yields a characterization for the bundle H → G → G/H to be trivial when π
1 (G/H) = 0. 相似文献
17.
As the main result, we show that if G is a finite group such that Γ(G) = Γ(2
F
4(q)), where q = 22m+1 for some m ≧ 1, then G has a unique nonabelian composition factor isomorphic to 2
F
4(q). We also show that if G is a finite group satisfying |G| =|2
F
4(q)| and Γ(G) = Γ(2
F
4(q)), then G ≅ 2
F
4(q). As a consequence of our result we give a new proof for a conjecture of W. Shi and J. Bi for 2
F
4(q).
The third author was supported in part by a grant from IPM (No. 87200022). 相似文献
18.
M. E. Palistrant 《Theoretical and Mathematical Physics》1999,119(3):761-777
We obtain the basic system of equations for a superconductivity theory of a system with a chaotically distributed paramagnetic
substitution impurity in which the Migdal theorem is violated (the condition ωD ≪E
F cannot be assumed). The electron-phonon and impurity diagrams and also the additional diagrams corresponding to intersections
of the electron-phonon and electron-impurity lines are taken into account. In the weak electron-phonon coupling limit, we
obtain an equation for the superconducting transition temperature TC that differs from the corresponding equation for the usual superconductors by renormalizations of TC0 and of the impurity scattering parameter, ρ. These quantities depend essentially on the Migdal parameter ωD/E
F and on the transferred momentum qc. We show that the decrease of TC with the increase of the impurity concentration is slowed, as compared with usual superconductors, to an extent determined
by m and qc. We also evaluate the isotopic coefficient α, whose behavior as a function of the impurity concentration depends on m and
qc.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 119, No. 3, pp 455–474, June, 1999 相似文献
19.
The prime graph of a finite group G is denoted by Γ(G). In this paper as the main result, we show that if G is a finite group such that Γ(G) = Γ(F
4(q)), where q = 2
n
> 2, then G has a unique nonabelian composition factor isomorphic to F
4(q). We also show that if G is a finite group satisfying |G| = |F
4(q)| and Γ(G) = Γ(F
4(q)), where q = 2
n
> 2, then G @ F4(q){G \cong F_4(q)}. As a consequence of our result we give a new proof for a conjecture of Shi and Bi for F
4(q) where q = 2
n
> 2. 相似文献
20.
We define the asymmetry constants(E) of a Banach spaceE, and show examples of finite-dimensional spaces with “large” asymmetry constants. IfE isn-dimensional,λ(E)17its projection constant and π
1(I
E
) the absolutely summing norm of the identity operatorI
E
, thenn≦λ(E)π1(I
E
)≤n(s(E))2. Similar equations linking thep-absolutely summing and the nuclear norms ofI
E
are established. We also obtain estimates on these norms, for example π2(I
E
)=√n.
The contribution of this author is a part of a Ph.D. Thesis prepared at the Hebrew University of Jerusalem under the supervision
of Professor J. Lindenstrauss whose guidance and valuable suggestions are gratefully acknowledged. 相似文献