共查询到20条相似文献,搜索用时 774 毫秒
1.
A.R Sourour 《Journal of Functional Analysis》1981,43(1):69-77
Let be a symmetric norm ideal of compact operators on Hilbert space , and assume that the finite rank operators are dense in and that is not the ideal of Hilbert-Schmidt operators. A linear transformation τ on is an isometry of onto itself if and only if there are unitary operators U and V on such that either τ(X) = UXV or τ(X) = UXtV, where Xt denotes the transpose of X with respect to a fixed orthonormal basis of . 相似文献
2.
Daryl Geller 《Journal of Functional Analysis》1980,36(2):205-254
We derive a usable characterization of the group FT (Fourier Transform) of Schwartz space on the Heisenberg group n, in terms of certain asymptotic series. To accomplish this we study in detail the FT of multiplication and differentiation operators on n, the relation of multiple Fourier series to the FT, and the process of group contraction on n. We use our characterization to solve a form of the division problem for convolution of n, which has application to Hardy space theory. 相似文献
3.
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
4.
G.Y.H Chi 《Journal of multivariate analysis》1973,3(1):71-92
Let (Ω, Σ, P) be a fixed complete probability space, the real Schwartz space, and its strong dual. and are partially ordered by and respectively, where is the positive cone of nonnegative functions in and its dual in . is a strict -cone and is normal, where is the family of all bounded subsets of . If X, Y are two random Schwartz distributions, then X ≤ Y if and only if Y(ω) ? X(ω) ∈ for almost all . Integrability of random Schwartz distributions and properties of such integrals are discussed. The monotone convergence theorem, the dominated convergence theorem, and Fatou's lemma are proved. The existence of conditional expectations of integrable random Schwartz distributions relative to a given sub σ-field of Σ is shown. Properties of conditional expectations are discussed and the conditional form of the monotone convergence theorem is proved. Sub(super)-martingale sequences are defined via the partial order relations introduced above, and a convergence theorem is given. The notion of a potential is introduced and the Riesz decomposition theorem is proved. 相似文献
5.
Let ′ be either the space ′1 of distributions of exponential growth or the space ′ of tempered distributions, and let ′C(′:′) be the space of convolution operators in ′. In each case ′ is the dual of a space of C∞-functions which are in ′C(′:′). We establish necessary and sufficient conditions on the Fourier transform of ? of S ? ′C(′:′) in order that every distribution u? ′C(′:′) with S1u? be in . If ′ = ′1, the condition is equivalent to S×H′1=H′1. 相似文献
6.
We find the automorphisms and the spectra of several different topological convolution algebras of C∞-functions on the real line. Starting with the convolution algebra of compactly supported C∞-functions, equipped with the usual LF-topology, we define a corresponding convolution algebra of C∞-functions of arbitrarily fast exponential decay at ∞; and convolution algebras of a given finite degree r of exponential decay at ∞. These algebras may be described topologically as “hyper Schwartz spaces.” With a natural Frechet topology, which we define, they get a structure as locally m-convex algebras. The continuous automorphisms and spectra of these algebras are described completely. We show that the algebra of C∞-functions of infinitly fast exponential decay at ∞, , on the one hand, and the algebra of C∞-functions of only a finite degree decay at ∞, r0, on the other hand, have quite different automorphisms, although = ∩rr0. As an application, we show that the conformal group is canonically represented as the full group of automorphisms of r0, and that this representation does not extend to a representation on the Banach algebra L1(). 相似文献
7.
Peter Hahn 《Journal of Functional Analysis》1979,31(3):263-271
Let ?L∞(S, μ) be a maximal abelian subalgebra of the factor on separable Hilbert space with modular involution J. (∪ JJ)″ is represented naturally as L∞(S × S, λ). If Takesaki's unitary equivalence relation ? S × S is not λ-null, it is a measure groupoid. If it is conull, and (∪ JJ)″ is maximal abelian, and are reconstructed by the σ-left regular representation procedure. Examples show that these hypotheses are not always satisfied. An application shows that the L∞ spectrum of a properly infinite ergodic transformation is null with respect to the L2 spectrum. 相似文献
8.
David Chillingworth 《Journal of Functional Analysis》1980,35(2):251-278
Let C be a Banach space, H a Hilbert space, and let F(C,H) be the space of C∞ functions f: C × H → R having Fredholm second derivative with respect to x at each (c, x) ?C × H for which ; here we write for . Say ? is of standard type if at all critical points of ?c it is locally equivalent (as an unfolding) to a quadratic form Q plus an elementary catastrophe on the kernel of Q. It is proved that if f?F (A × B, H) satisfies a certain ‘general position’ condition, and dim B ? 5, then for most a?A the function fo?F(B,H) is of standard type. Using this it is shown that those f?F(B,H) of standard type form an open dense set in F(B,H) with the Whitney topology. Thus both results are Hilbert-space versions of Thom's theorem for catastrophes in n. 相似文献
9.
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
10.
Gordon S. Woodward 《Journal of Functional Analysis》1974,16(2):205-220
Suppose G is a locally compact noncompact group. For abelian such G's, it is shown in this paper that L1(G), C(G), and L∞(G) always have discontinuous translation-invariant linear forms(TILF's) while C0(G) and Lp(G) for 1 < p < ∞ have such forms if and only if is a torsion group for some open σ-compact subgroup H of . For σ-compact amenable G's, all the above spaces have discontinuous left TILF's. 相似文献
11.
Harrie Hendriks 《Journal of Pure and Applied Algebra》1978,10(3):227-232
Let G be a finitely generated accessible group. We will study the homology of G with coefficients in the left G-module H1(G;[G]). This G-module may be identified with the G-module of continuous functions with values in on the G-space of ends of G, quotiented by the constant functions. The main result is as follows: Suppose G is infinite, then the abelian group H1(G;H1(G;[G])) has rank 1 if G has a free subgroup of finite index and it has rank 0 if G has not. 相似文献
12.
Paul Milnes 《Journal of Mathematical Analysis and Applications》1978,65(1):32-43
Recently Lau [15] generalized a result of Yeadon [25]. In the present paper we generalize Yeadon's result in another direction recasting it as a theorem of ergodic type. We call the notion of ergodicity required left mean-ergodicity and show how it relates to the mean-ergodicity of Nagel [21]. Connections with the existence of invariant means on spaces of continuous functions on semitopological semigroups S are made, connections concerning, among other things, a fixed point theorem of Mitchell [20] and Schwartz's property P of W1-algebras [22]. For example, if (S) is a certain subspace of C(S) (which was considered by Mitchell and is of almost periodic type, i.e., the right translates of a member of (S) satisfy a compactness condition), then the assumption that (S) has a left invariant mean is equivalent to the assumption that every representation of S of a certain kind by operators on a linear topological space X is left mean-ergodic. An analog involving the existence of a (left and right) invariant mean on (S) is given, and we show our methods restrict in the Banach space setting to give short direct proofs of some results in [4], results involving the existence of an invariant mean on the weakly almost periodic functions on S or on the almost periodic functions on S. An ergodic theorem of Lloyd [16] is generalized, and a number of examples are presented. 相似文献
13.
To say that a commutative ring with unit is coherent amounts to saying, in case has no divisors of zero, that the intersection of two finitely generated ideals in is finitely generated. We prove that the ring H∞ of bounded analytic functions in the unit disc is coherent, while the disc algebra A is not coherent. For any positive measure μ, L∞(μ) is coherent. 相似文献
14.
Steven Ziskind 《Journal of Functional Analysis》1976,21(4):380-388
Let H∞(Δ) denote the Banach algebra of bounded analytic functions on the open unit disc, let denote its maximal ideal space, and let ? denote its Shilov boundary. D. J. Newman has shown that a homomorphism ? in will be in ? if and only if ? is unimodular on all Blaschke products. We answer a question of K. Hoffman by showing that ? will be in ? if and only if ? is unimodular on every Blaschke product whose zero set is an interpolating sequence. Our method is based on a construction due to L. Carleson, originally developed for the proof of the Corona theorem. 相似文献
15.
Let P denote a cubic integral polynomial, and let D(P) and H(P) denote the discriminant and height of P, respectively. Let N(Q,X) be the number of cubic integral polynomials P such that H(P) ≤ Q and |D(P)| ≤ X. We obtain an asymptotic formula of N(Q,X) for Q 14/5 ? X ? Q 4 and Q → +∞. Using this result, for 0 ≤ η ≤ 9/10, we find the asymptotic value of $$ \sum\limits_{{\begin{array}{*{20}{c}} {H(P)\leq Q} \\ {1\leq \left| {D(P)} \right|\ll {Q^{{4-\eta }}}} \\ \end{array}}} {{{{\left| {D(P)} \right|}}^{{-{1 \left/ {2} \right.}}}}}, $$ where the sum is taken over irreducible integral polynomials and Q → +∞. This improves upon a result of Davenport, who dealt with the case η = 0. 相似文献
16.
Weita Chang 《Journal of Functional Analysis》1979,34(3):481-492
Let G be a noncompact semisimple Lie group with finite center and H an open subgroup of the fixed point group of an involution of G. becomes a pseudo-Riemannian manifold. We prove that the Laplacian P on is globally solvable in the sense that . This generalizes the global solvability of the Casimir operators on non-compact semisimple Lie groups with finite center due to J. Rauch and D. Wigner. 相似文献
17.
Harry Dym 《Journal of Functional Analysis》1978,28(1):33-57
Let PT denote the orthogonal projection of L2(R1, dΔ) onto the space of entire functions of exponential type ? T which are square summable on the line with respect to the measure , and let G denote the operator of multiplication by a suitably restricted complex valued function g. It is shown that if is summable, if is locally summable, and if belongs to the span in L∞ of e?iyTH∞:T ? 0, in which h is chosen to be an outer function and h#(γ) agrees with the complex conjugate of h(γ) on the line, then exists and is independent of h for every positive integer n. This extends the range of validity of a formula due to Mark Kac who evaluated this limit in the special case h = 1 using a different formalism. It also extends earlier results of the author which were established under more stringent conditions on h. The conclusions are based in part upon a preliminary study of a more general class of projections. 相似文献
18.
Stephen M. Paneitz 《Journal of Functional Analysis》1981,41(3):315-326
Let Sp() be the symplectic group for a complex Hibert space . Its Lie algebra sp() contains an open invariant convex cone C0; each element of C0 commutes with a unique sympletic complex structure. The Cayley transform : X∈ sp()→(I + X)1∈ Sp() is analyzed and compared with the exponential mapping. As an application we consider equations of the form is strongly continuous, and show that if ∝?∞∞ ∥A(t)∥ dt < 2 and ∝? t8∞A(t) dt?C0, the (scattering) operator , where St′(t) is the solution such that St′(t′) = I, is in the range of restricted to C0. It follows that S leaves invariant a unique complex structure; in particular, it is conjugate in Sp() to a unitary operator. 相似文献
19.
If A and B are self-adjoint operators, this paper shows that A and B have order isomorphic invariant subspace lattices if and only if there are Borel subsets E and F of σ(A) and σ(B), respectively, whose complements have spectral measure zero, and there is a bijective function φ: E → F such that (i) Δ is a Borel subset of E if and only if φ(Δ) is a Borel subset of F; (ii) a Borel subset Δ of E has A-spectral measure zero if and only if φ(Δ) has B-spectral measure zero; (iii) B is unitarily equivalent to φ(A). If A is any self-adjoint operator, there is an associated function κA : ∪ {∞} → ( ∪ {0, ∞}) × {0,1} defined in this paper. If denotes the collection of all functions from ∪ {∞} into ( ∪ {0,∞}) × {0,1}, then is a parameter space for the isomorphism classes of the invariant subspace lattices of self-adjoint operators. That is, two self-adjoint operators A and B have isomorphic invariant subspace lattices if and only if κA = κB. The paper ends with some comments on the corresponding problem for normal operators. 相似文献