共查询到20条相似文献,搜索用时 31 毫秒
1.
Rahman Younis 《Journal of Functional Analysis》1981,44(3):381-387
The main result of this paper is that if F is a closed subset of the unit circle, then is an M-ideal of . Consequently, if then ? has a closest element in H∞ + LF∞. Furthermore, if is not the dual of any Banach space. 相似文献
2.
N.J Kalton 《Journal of Functional Analysis》1981,42(3):299-337
We prove a number of results concerning isomorphisms between spaces of the type Lp(X), where X is a separable p-Banach space and 0 < p < 1. Our results imply that the quotient of Lp([0, 1] × [0, 1]) by the subspace of functions depending only on the first variable is not isomorphic to Lp, answering a question of N. T. Peck. More generally if 0 is a sub-σ-algebra of the Borel sets of [0, 1], then , 0) is isomorphic to Lp if and only if Lp([0, 1], B0) is complemented. We also show that Lp has, up to isomorphism, at most one complemented subspace non-isomorphic to Lp and classify completely those spaces X for which . In particular if then or is finite-dimensional. If X has trivial dual and . 相似文献
3.
The spaces in the title are associated to a fixed representing measure m for a fixed character on a uniform algebra. It is proved that the set of representing measures for that character which are absolutely continuous with respect to m is weakly relatively compact if and only if each m-negligible closed set in the maximal ideal space of L∞ is contained in an m-negligible peak set for H∞. J. Chaumat's characterization of weakly relatively compact subsets in therefore remains true, and is complete, under the first conditions. In this paper we also give a direct proof. From this we obtain that has the Dunford-Pettis property. 相似文献
4.
5.
Walter Rudin 《Journal of Functional Analysis》1983,50(1):100-126
Let B be the open unit ball of n, n > 1. Let I (for “inner”) be the set of all u ? H °(B) that have a.e. on the boundary S of B. Aleksandrov proved recently that there exist nonconstant u ? I. This paper strengthens his basic theorem and provides further information about I and the algebra Q generated by I. Let XY be the finite linear span of products xy, x ? X, y ? Y, and let be the norm closure, in L∞ = L∞(S), of X. Some results: set I is dense in the unit ball of H∞(B) in the compact-open topology. On is weak1-dense in does not contain . (When .) Every unimodular is a pointwise limit a.e. of products . The zeros of every in the ball algebra (but not of every H∞-function) can be matched by those of some u ? I, as can any finite number of derivatives at 0 if . However, cannot be bounded in B if u ? I is non-constant. 相似文献
6.
Ep de Jonge 《Journal of Functional Analysis》1976,23(2):119-134
Under the condition that , (the set of singular functionals on a normed Köthe space Lθ) is an abstract L-space, it is proved in this paper that there exists a set of purely finitely additive measures θ such that ? holds. It follows that is an abstract L-space if and only if is Riesz isomorphic and isometric with a band in . 相似文献
7.
Nicolae Dinculeanu 《Journal of Functional Analysis》1973,12(3):229-235
Let (X, ∑, μ) be a measure space and S be a semigroup of measure-preserving transformations T:X → X. In case μ(X) < ∞, Aribaud [1] proved the existence of a positive contractive projection P of L1(μ) such that for every belongs to the closure of the convex hull of the set {}. In this paper we extend this result in three directions: we consider infinite measure spaces, vector-valued functions, and Lp spaces with 1 ? p < ∞, and prove that P is in fact the conditional expectation with respect to the σ-algebra Λ of sets of ∑ which are invariant with respect to all T?S. 相似文献
8.
Palle E.T Jørgensen 《Journal of Functional Analysis》1975,20(2):105-135
In this paper we apply the theory of second-order partial differential operators with nonnegative characteristic form to representations of Lie groups. We are concerned with a continuous representation U of a Lie group G in a Banach space . Let be the enveloping algebra of G, and let dU be the infinitesimal homomorphism of into operators with the Gårding vectors as a common invariant domain. We study elements in of the form with the Xj,'s in the Lie algebra .If the elements X0, X1,…, Xr generate as a Lie algebra then we show that the space of C∞-vectors for U is precisely equal to the C∞-vectors for the closure . This result is applied to obtain estimates for differential operators.The operator is the infinitesimal generator of a strongly continuous semigroup of operators in . If X0 = 0 we show that this semigroup can be analytically continued to complex time ζ with Re ζ > 0. The generalized heat kernels of these semigroups are computed. A space of rapidly decreasing functions on G is introduced in order to treat the heat kernels.For unitary representations we show essential self-adjointness of all operators with X0 in the real linear span of the Xj's. An application to quantum field theory is given.Finally, the new characterization of the C∞-vectors is applied to a construction of a counterexample to a conjecture on exponentiation of operator Lie algebras.Our results on semigroups of exponential growth, and on the space of C∞ vectors for a group representation can be viewed as generalizations of various results due to Nelson-Stinespring [18], and Poulsen [19], who prove essential self-adjointness and a priori estimates, respectively, for the sum of the squares of elements in a basis for (the Laplace operator). The work of Hörmander [11] and Bony [3] on degenerate-elliptic (hypoelliptic) operators supplies the technical basis for this generalization. The important feature is that elliptic regularity is too crude a tool for controlling commutators. With the aid of the above-mentioned hypoellipticity results we are able to “control” the (finite dimensional) Lie algebra generated by a given set of differential operators. 相似文献
9.
Wolfgang Lusky 《Journal of Functional Analysis》1985,62(1):1-7
It is shown that every separable Banach space X containing a subspace isomorphic to c0 has a subspace Y with basis such that and the latter space has a shrinking basis and an unconditional FDD. Moreover, it is shown that X ⊕ C∞ has a basis if X has the bounded approximation property. 相似文献
10.
David S. Jerison 《Journal of Functional Analysis》1981,43(2):224-257
Let L = ∑j = 1mXj2 be sum of squares of vector fields in n satisfying a Hörmander condition of order 2: span{Xj, [Xi, Xj]} is the full tangent space at each point. A point x??D of a smooth domain D is characteristic if X1,…, Xm are all tangent to ?D at x. We prove sharp estimates in non-isotropic Lipschitz classes for the Dirichlet problem near (generic) isolated characteristic points in two special cases: (a) The Grushin operator in 2. (b) The real part of the Kohn Laplacian on the Heisenberg group in 2n + 1. In contrast to non-characteristic points, C∞ regularity may fail at a characteristic point. The precise order of regularity depends on the shape of ?D at x. 相似文献
11.
Larry W. Cusick 《Topology and its Applications》1985,21(1):9-18
We show that if X is a finite CW-complex admitting a fixed point free involution then there is a singly graded spectral sequence with and . As an application we prove that for any n > 0 there is a natural number k(n) such that if n > k(n) and X is a homotopy , then X will not admit a fixed point free involution. 相似文献
12.
Hans G Kaper 《Journal of Mathematical Analysis and Applications》1978,63(3):691-718
In this article we discuss the solution of boundary value problems which are described by the linear integrodifferential equation , where t∈J?, x∈. We interpret the equation in functional form as an ordinary differential equation for the mapping u:J→L2(R,μ), where L2(R,μ) is a weighted L2-space. Emphasis is on the constructive aspects of the solution and on finding representations of the relevant isomorphisms. 相似文献
13.
Rainer Wittmann 《Statistics & probability letters》1985,3(3):131-133
We apply a moment inequality of H.P. Rosenthal to get various generalizations of a theorem of Brunk-Chung-Prohoroff. In particular, we show that the strong law hols provided and for one p ? 1. 相似文献
14.
Let K1, K2,... be a sequence of regular graphs with degree v?2 such that n(Xi)→∞ and ck(Xi)/n(Xi)→0 as i∞ for each k?3, where n(Xi) is the order of Xi, and ck(Xi) is the number of k- cycles in X1. We determine the limiting probability density f(x) for the eigenvalues of X>i as i→∞. It turns out that for ?x??2, otherwise It is further shown that f(x) is the expected eigenvalue distribution for every large randomly chosen labeled regular graph with degree v. 相似文献
15.
Robert Chen 《Journal of multivariate analysis》1978,8(2):328-333
Let {Xn}n≥1 be a sequence of independent and identically distributed random variables. For each integer n ≥ 1 and positive constants r, t, and ?, let Sn = Σj=1nXj and . In this paper, we prove that (1) lim?→0+?α(r?1)E{N∞(r, t, ?)} = K(r, t) if E(X1) = 0, Var(X1) = 1, and E(| X1 |t) < ∞, where 2 ≤ t < 2r ≤ 2t, , and ; (2) if 2 < t < 4, E(X1) = 0, Var(X1) > 0, and E(|X1|t) < ∞, where G(t, ?) = E{N∞(t, t, ?)} = Σn=1∞nt?2P{| Sn | > ?n} → ∞ as ? → 0+ and , i.e., H(t, ?) goes to infinity much faster than G(t, ?) as ? → 0+ if 2 < t < 4, E(X1) = 0, Var(X1) > 0, and E(| X1 |t) < ∞. Our results provide us with a much better and deeper understanding of the tail probability of a distribution. 相似文献
16.
17.
We study generalizations of Ramsey theorem to systems of finite subsets of ω. A system of finite subsets of ω is called to be Ramsey if for every partition =1∪2 there exists an infinite set Y?ω such that . We give some sufficient conditions for a system to be Ramsey. We also prove a theorem which concerns partitions into infinitely many classes. This may be regarded as a common generalization of Erdös-Rado and Nash-Williams theorems. 相似文献
18.
Georg Neuhaus 《Journal of multivariate analysis》1980,10(1):19-25
Let X be a Gaussian rv with values in a separable Hilbert space H having a covariance operator R of the form , where L0, A are linear operators on H. A method is given for computing in terms of and A the distribution of |X|2, |·| being the norm in H. The result is applied to the evaluation of the asymptotic distribution of Cramér-von Mises statistics when parameters are present. L0 corresponds to the case where the true underlying parameter is known and A represents the effect of estimating the unknown parameter. 相似文献
19.
Bernard Heinkel 《Journal of multivariate analysis》1983,13(2):353-360
It is shown that for the elements X of a large class of subgaussian random variables with values in (C(S), |·|∞) the existence of a probability measure λ on S such that: (where ψ denotes the inverse function of x → exp x2L2x) is sufficient to imply that X satisfies the law of the iterated logarithm. 相似文献
20.
R.A. Doney 《Stochastic Processes and their Applications》1982,12(2):203-214
Let T+ denote the first increasing ladder epoch in a random walk with a typical step-length X. It is known that for a large class of random walks with E(X)=0,E(X2)=∞, and the right-hand tail of the distribution function of X asymptotically larger than the left-hand tail, as n→∞, with 1<β<2 and L+ slowly varying, if and only if as x→+∞, with L slowly varying. In this paper it is shown how the asymptotic behaviour of L determines the asymptotic behaviour of L+ and vice versa. As a by-product, it follows that a certain class of random walks which are in the domain of attraction of one-sided stable laws is such that the down-going ladder height distribution has finite mean. 相似文献