共查询到20条相似文献,搜索用时 15 毫秒
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We give several characterizations of those Banach spaces X such that the dual contains a complemented subspace isomorphic to . We investigate operators on separable ∞ spaces whose adjoints have nonseparable ranges and apply our results to obtain a structure theorem for ∞ spaces whose duals are not isomorphic to l1(Γ). 相似文献
3.
Let , let , where g2 and g3 are coefficients of the elliptic curve: Y2 = 4X3 ? g2X ? g3 over a finite field and Δ = g23 ? 27g32 and let . Then the p-adic cohomology theory will be applied to compute explicitly the zeta matrices of the elliptic curves, induced by the pth power map on the free -module . Main results are; Theorem 1.1: X2dY and YdX are basis elements for ; Theorem 1.2: YdX, X2dY, Y?1dX, Y?2dX and XY?2dX are basis elements for , where is a lifting of X, and all the necessary recursive formulas for this explicit computation are given. 相似文献
4.
R.R Smith 《Journal of Functional Analysis》1979,32(3):269-271
M-ideals in a commutative Banach algebra A are shown to correspond to certain hermitian central projections in , and thus possess bounded approximate identities. This leads to a new characterization of M-ideals in function algebras. 相似文献
5.
Kenneth R Davidson 《Journal of Functional Analysis》1982,48(1):20-42
Given a commuting pair 1, 2 of abelian subalgebras of the Calkin algebra, we look for a commuting pair 1,2 of subalgebras of which project onto 1 and 2. We do not insist that i, be abelian, so i, may contain nontrivial compact operators. If X is the joint spectrum σ(1, 2), it is shown that the existence of a pair 1, 2 depends only on the element τ in Ext(X) determined by 1, 2. The set L(X) of those τ in Ext(X) which “lift” in this sense is shown to be a subgroup of Ext(X) when Ext(X) is Hausdorff, and also when i are singly generated. In this latter case, L(X) can be explicitly calculated for large classes of joint spectra. These results are applied to lift certain pairs of commuting elements of the Calkin algebra to pairs of commuting operators. 相似文献
6.
Let A be a -algebra, B be a -subalgebra of A, and φ be a factorial state of B. Sometimes, φ may be extended to a factorial state of A by a tensor product method of Sakai (“-algebras and -algebras, Springer-Verlag, Berlin/Heidelberg/ New York 1971”). Sometimes, there is a weak expectation of A into , and then factorial extensions may be found by a method of Sakai and Tsui (Yokohama Math. J.29 (1981), 157–160). These two methods are shown to have the same effect, and the factorial extensions produced by them are analysed. 相似文献
7.
The main result is that every weakly compact operator between Banach spaces factors through a reflexive Banach space. Applications of the result and technique of proof include new results (e.g., separable conjugate spaces embed isomorphically in spaces with boundedly complete bases; convex weakly compact sets are affinely homeomorphic to sets in a reflexive space) and simple proofs of known results (e.g., there is a reflexive space failing the Banach-Saks property; if X is separable, then for some Z; there is a separable space which does not contain l1 whose dual is nonseparable). 相似文献
8.
Thierry Gaspari 《Comptes Rendus Mathematique》2002,334(3):189-194
We study the range of the derivative of a Frechet differentiable bump. X is an infinite dimensional separable Cp-smooth Banach space. We first prove that any connected open subset of containing 0 is the range of the derivative of a Cp-bump. Next, analytic subsets of which satisfy a natural linkage condition are the range of the derivative of a C1-bump. We find analogues of these results in finite dimensions. We finally show that is the closure of its interior, if f is a C2-bump on . To cite this article: T. Gaspari, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 189–194. 相似文献
9.
Marc P Thomas 《Journal of Functional Analysis》1981,41(2):204-212
One says a commutative radical Banach algebra A has a lower bound if there is a lower growth condition on for all nonzero elements x in A. If A is a separable algebra we give necessary and sufficient conditions for A to possess a lower bound. 相似文献
10.
Hsin Chu 《Journal of Mathematical Analysis and Applications》1982,85(2):566-583
Let X and Y be Banach spaces, ; P is said to be strongly ?-accretive if for some c > 0 and each x,y?X. These mappings constitute a generalization simultaneously of monotone mappings () and accretive mappings (when Y = X). By applying a theorem of 1. Ekeland, it is shown that a localized class of these mappings must be surjective under appropriate geometric assumptions on and continuity assumptions on P. The results generalize two theorems of F. E. Browder and the proofs further refine the methodology for dealing with such mappings. 相似文献
11.
Let A be a linear subspace of complex C(X) which separates points and contains the constants. Hustad has shown that to each complex linear functional L in there corresponds a complex regular Borel measure μ “supported by” the Choquet boundary ?A of A which represents L and satisfies ∥ μ ∥ = ∥ L ∥. We give a number of conditions on the dual ball of A which are necessary and sufficient for each L in to be represented by a unique such measure μ. 相似文献
12.
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
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Let (, G, α) be a dynamical system and let δ be a closed 1 derivation in which commutes with α and satisfies G ? ker(δ). If is a separable Type I algebra and G is a second countable compact group, then δ generates a strongly continuous one parameter group of 1 automorphisms of . 相似文献
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In this paper, we establish the following results: Let A be a square matrix of rank r. Then (a) is idempotent of rank r, and trrA (defined as the sum of the principal minors of order r in A) is one iff A is Hermitian idempotent. (b) As=At for some positive integers s≠t, and trA=rankA iff A is idempotent. (c) for some integers s≠t iff is idempotent, while for some integers s≠0 iff . (d) for some integers s≠t and rankA=trA iff A is Hermitian idempotent, while for some integer s iff A is Hermitian. Here indicates the conjugate transpose of A, and P-α is defined iff (P+)α=(Pα)+ for all positive integers α and P+ is the Moore-Penrose inverse of P. 相似文献
15.
If is a weakly compactly generated (WCG) Banach space, then X admits an equivalent C1-smooth norm. If a WCG Banach space X admits a Ck-smooth function with bounded support, then X admits Ck-smooth partitions of unity. 相似文献
16.
Let 1 < p ? 2 ? q < ∞ and X be either a Banach lattice which is p-convex and q-concave or a unitary ideal of operators on l2 which is modeled on a symmetric space which is p-convex and q-concave. If E ?X is any n-dimensional subspace, then both the distance from E to and the relative projection constant of E in X are dominated by . 相似文献
17.
Herbert Halpern 《Journal of Functional Analysis》1980,36(3):313-342
Let be a von Neumann algebra, let σ be a strongly continuous representation of the locally compact abelian group G as 1-automorphisms of . Let M(σ) be the Banach algebra of bounded linear operators on generated by ∝ σtdμ(t) (μ?M(G)). Then it is shown that M(σ) is semisimple whenever either (i) has a σ-invariant faithful, normal, semifinite, weight (ii) σ is an inner representation or (iii) G is discrete and each σt is inner. It is shown that the Banach algebra L(σ) generated by is semisimple if a is an integrable representation. Furthermore, if σ is an inner representation with compact spectrum, it is shown that L(σ) is embedded in a commutative, semisimple, regular Banach algebra with isometric involution that is generated by projections. This algebra is contained in the ultraweakly continuous linear operators on . Also the spectral subspaces of σ are given in terms of projections. 相似文献
18.
Steven F Arnold 《Statistics & probability letters》1985,3(5):275-279
Suppose that a statistical decision problem is invariant under a group of transformations g?G. T (X) is equivariant if there exists such that . We show that the minimal sufficient statistic is equivalent and that if T(X) is an equivariant sufficient statistics and d(X) is invariant under G, then is invariant under . 相似文献
19.
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
20.
Richard Rochberg 《Journal of Functional Analysis》1973,13(2):154-172
Let A(S) be the sup-normed Banach algebra of analytic functions with continuous boundary values on the compact bordered Riemann surface S.For (?) in , the colength of (?) is defined by . Colength is shown to induce a norm on the cohomology group H1(S,R) dual to the norm induced on the homology group H1(S,R) by harmonic length, or, equivalently, dual to the norm on Re A(S)⊥.The existence and uniqueness of extremal functions for the colength functional is demonstrated. The aforementioned norms are shown to determine the conformal structure of S (up to reflection) and to be related to the mapping properties of S. 相似文献