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1.
Casazza  P.G.  Nielsen  N.J. 《Positivity》2001,5(4):297-321
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 This result is originally due to G. Pisier (unpublished), but our proof is different.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.
A=(a ij) i j=1k-o ,a ij . :
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3.
By using the classical Hadamard theorem, we obtain an exact (in a certain sense) inequality for the best polynomial approximations of an analytic function f(z) from the Hardy space H p, p 1, in disks of radii , 1, and 2, 0 < 1 < < 2 < 1.  相似文献   

4.
N. V. Kuznetsov's summation formula is generalized to the case of a discrete subgroup GSL2() and a system of multiplicators , satisfying certain not too restrictive conditions. In the arithmetic cases, when G is a congruence-subgroup in SL2(), these conditions are satisfied. N. V. Kuznetsov's formula has been proved for the case G=SL2()., =1.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 82, pp. 103–135, 1979.  相似文献   

5.
K. M. Koh  K. S. Poh 《Order》1985,1(3):285-294
Let (G) and V(G) be, respectively, the closed-set lattice and the vertex set of a graph G. Any lattice isomorphism : V(G)(G) induces a bijection : V(G)V(G) such that for each x in V(G), (x)=x' in V(G') iff ({x})={x'}. A graph G is strongly sensitive if for any graph G' and any lattice isomorphism : (G)(G), the bijection induced by is a graph isomorphism of G onto G'. In this paper we present some sufficient conditions for graphs to be strongly sensitive and prove in particular that all C 4-free graphs and all covering graphs of finite lattices are strongly sensitive.  相似文献   

6.
Let G(k) be the Chevalley group of normal type associated with a root system G = , or of twisted type G = m,m = 2,3, over a field K. Its root subgroups Xs, for all possible s G+, generate a maximal unipotent subgroup U = UG(k) if p = charK < 0, U is a Sylow p-subgroup of G(K). We examine G and K for which there exists a paired intersection U U9, g G(K), which is not conjugate in G(K) to a normal subgroup of U. If K is a finite field, this is equivalent to a condition that the normalizer of U U9 in G(K)has a p-multiple index. Put p() = max(r,r)/(s,s) | r,s . We prove a statement (Theorem 1) saying the following. Let G(K) be a Chevalley group of Lie rank greater than 1 over a finite field K of characteristic p and U be its Sylow p-subgroup equal to UG(K); also, either G = and p() is distinct from p and 1, or G(K) is a twisted group. Then G(K) contains a monomial element n such that the normalizer U of Un in G(K) has a p-multiple index. Let K be an associative commutative ring with unity and (K,J) be a congruence subgroup of the Chevalley group (K) modulo a nilpotent ideal J. We examine an hypercentral series 1 Z1 Z2 ... Zc-1 of the group U(K) (K,J). Theorem 2 shows that under an extra restriction on the quotient (Jt : J) of ideals, central series are related via Zi = Tc-iC, 1 i < c, where C is a subgroup of central diagonal elements. Such a connection exists, in particular, if K = Zpm and J = (pd), 1 d < m, d| m.  相似文献   

7.
Let X/Fp be an Artin–Schreier curve defined by the affine equation y p y=f(x) where f(x)Fp[x] is monic of degree d. In this paper we develop a method for estimating the first slope of the Newton polygon of X. Denote this first slope by NP1(X/Fp). We use our method to prove that if p>d2 then NP1(X/Fp)(p–1)/d/(p–1). If p>2d4, we give a sufficient condition for the equality to hold.  相似文献   

8.
9.
Let V be a vector space over the commutative field K such that char K 2 2 dim V , and let Q:V K be a quadratic form of rank 2. The pair (A(V,K),Q), consisting of the affine space A(V,K) and the congruence relation Q, defined by (a,b)Q (c,d) Q(a–b) = Q(c–d) (a,b),(c,d) V×V, is called an affine-metric fano-space of rank 2. In this paper, such spaces are characterized by three simple geometrical properties.  相似文献   

10.
11.
In this paper we give conditions under which we can obtain explicit analytic expressions of the fundamental sublinear functional PK of the family of means K=[G]J where [G] is a subset of G-invariant means, G a semigroup of operators on 1 and J a saturated set of means. Such conditions allow us to assure that [G]J.We characterize the set of the almost convergent sequences related to the family K by means of the same functional pK. We obtain also pK in terms of pJ when pJ is known. This allow us to give different expressions of the same functional pK when the family J changes and from which several examples are given.  相似文献   

12.
{n} a n n , s n n- , n -n- (, 1)- . . . -, . , «|s2n+1–s 2 n¦< . .» «¦ n n–1¦< . .» . s. , {a n } 0, a n/n<, {a n } , {it|n¦<. , , -.  相似文献   

13.
The solution of the following problems is offered. Suppose a multiset J (¦J¦=p) is given. For each pair of elements and J, a number 1 P is given. Moreover, if 1 < x<p then x is undefined. If x=1, then x=p. Problem 1. Find the permutation 1...F of elements of the multiset J satisfying the following conditions. Let i, i=. If i,j < x, thenj <i. If i,j > x, then i<j. Such a permutation is called a PC-schedule. Problem 2. Find a PC-schedule in which the following property holds: if i < x < j, i=, j=, then. Such a PC-schedule is called an SC-schedule. The conditions under which these problems have solutions are studied. For their solution an algorithm of shifts is used with the complexity O(¦B(J)¦2¦J¦).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 124, pp. 44–72, 1983.  相似文献   

14.
It is shown that the algebra of the multipliers of the space p (1<<) contains the closed subalgebra Cp+H p , which coincides with the Douglas algebra C + H for =2. It is proved that a Toeplitz operator with symbol from Cp+H p is Fredholm on p if and only if its symbol is invertible in Cp+H p .Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 157, pp. 124–128, 1987.The authors are grateful to V. I. Vasyunin for assistance.  相似文献   

15.
Let G and {kj} be the domain and the array mentioned in the title (the boundary of the domain is assumed to be rectifiable). One describes a general scheme for the approximation of fonctionsf in the domain G, representable in the form f(z)=(2i)–1g()(–z)–1d, where g Lz (G), by a sequence of rational fractions. The characteristic feature of this scheme is the fact that the poles k of the fraction lie in the k-th row of the array {kj}. There is given a condition on {kj}, necessary and sufficient in order that each functionf, of the kind described above, should admit a uniform approximation inside G with the aid of the indicated scheme. In the case when this condition is not satisfied and \G.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 170, pp. 254–273, 1989.  相似文献   

16.
The behavior of the poles zn(), n=1,2,... of the scattering matrix of the operatorl u=–u(x), x , (u/n)+(x)u|=0 as 0 is considered. It is proved that |zn()–zn|=0((1/2)qn), where qn is the order of the pole of the scattering matrix for the operator 0u=–u, u/=0.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 117, pp. 183–191, 1981.  相似文献   

17.
We prove the completeness and decidability of the Hornlike sequents, specifically, the socalled D2sequents (of the firstorder linear temporal logic) considered in the author's paper [Lith. Math. J., 41(3), 266–281 (2001)]. In this paper, with the help of the infinitary calculus GL, grounded by the author in his earlier papers, for D2sequents we construct a D2Sat calculus of the socalled saturated type consisting of decidable deductive procedures replacing the omegarule for the always operator. In the present paper, in order to prove the completeness and decidability of the calculus D2Sat, we construct the socalled invariant decidable calculus D2IN. We prove the equivalence of the calculi D2IN, D2Sat, and G L ** for the socalled saturated D2sequents. From this equivalence, by reducing an arbitrary D2sequent to a saturated D2sequent, and also from the completeness of the G L ** calculus and decidability of the invariant calculus D2IN, we deduce the completeness and decidability of the calculus D2Sat in the class of D2sequents.  相似文献   

18.
If T is a completely nonunitary contraction on a Hilbert space and L is its invariant subspace corresponding to a regular factorization of its characteristic function = , then L is hyperinvariant if and only if the following two conditions are fulfilled: (1) supp * supp is of Lebesgue measure zero; (2) for every pair A H (E E) and A * H (E * E *) intertwining by , i.e., such that A =A *, there exists a function A F H (F F) intertwining with A by and with A * by , i.e., such that A = A F and A F = A *. Bibliography: 4 titles.  相似文献   

19.
Let D be a subgroup of the group G. The lattice of intermediate subgroups is studied. The subgroup F (D F G) is said to be D-complete, if DF=u:u F>=F. Let F be the subset of all D-complete intermediate subgroups. The system {F, NG(F)} is a fan for D in G (RZhMat, 1980, 5A208) if and only if Dx> is a D-complete subgroup for any x G. The set {Fga} coincides with the collection of subgroups of the form DA (1 A C G) if and only if for any x G the subgroup D, Dx is D-complete. The last condition holds, for example, for a pronormal subgroup D.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 103, pp. 13–19, 1980.  相似文献   

20.
In the beginning of the paper, we review the summation formulas for the Fourier coefficients of holomorphic cusp forms for , =SL(2,), associated with L-functions of three and four Hecke eigenforms. Continuing the known works on the L-functions Lf,,(s) of three Hecke eigenforms, we prove their new properties in the special case of Lf,,(s). These results are applied to proving an analogue of the Siegel theorem for the L-function Lf(s) of the Hecke eigenform f(z) for (with respect to weight) and to deriving a new summation formula. Let f(z) be a Hecke eigenform for of even weight 2k with Fourier expansion . We study a weight-uniform analogue of the Hardy problem on the behavior of the sum p&#x2264;xa(p) log p and prove new estimates from above for the sum nxa(F(n))2, where F(x) is a polynomial with integral coefficients of special form (in particular, F(x) is an Abelian polynomial). Finally, we obtain the lower estimate
where L4(s) is the fourth symmetric power of the L-function Lf(s) and c is a constant. Bibliography: 43 titles.Dedicated to the 90th anniversary of G. M. Goluzin's birthTranslated fromZapiski Nauchnykh Seminarov POMI, Vol. 237, 1997, pp. 194–226.The research was partially supported by the Russian Foundation for Basic Research, grant 96-01-00663.  相似文献   

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