共查询到20条相似文献,搜索用时 15 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.
Tomas P Schonbek 《Journal of Mathematical Analysis and Applications》1977,58(3):527-540
Let be a Banach space; S and T bounded scalar-type operators in . Define Δ on the space of bounded operators on by ΔX = TX ? XS if X is a bounded operator. We set up a calculus for Δ which allows us to consider f(Δ), for f a complex-valued bounded Borel measurable function on the spectrum of Δ, as an operator in the space of bounded operators whose domain is a subspace of operators which we call measure generating. This calculus is used to obtain some results on when the kernel of Δ is a complemented subspace of the space of bounded operators on . 相似文献
3.
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
4.
A. Voros 《Journal of Functional Analysis》1978,29(1):104-132
We discuss in detail the regularity properties of a class of pseudodifferential operators on l introduced by Grossmann, Loupias, and Stein, which are more regular and more symmetrical than usual pseudodifferential operators. Those operators that are self-adjoint form a suitable class of smooth observables for a nonrelativistic quantum theory. If their symbols are allowed to depend smoothly upon Planck's constant , those operators provide the framework for regular asymptotics expansions as of quantum mechanics around classical mechanics. 相似文献
5.
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
6.
Gilles Pisier 《Journal of Functional Analysis》1978,29(3):397-415
We study a conjecture of Grothendieck on bilinear forms on a C1-algebra . We prove that every “approximable” operator from into 1 factors through a Hilbert space, and we describe the factorization. In the commutative case, this is known as Grothendieck's theorem. These results enable us to prove a conjecture of Ringrose on operators on a C1-algebra. In the Appendix, we present a new proof of Grothendieck's inequality which gives an improved upper bound for the so-called Grothendieck constant kG. 相似文献
7.
Necessary and sufficient conditions are found for a multiplier operator to be bounded on L2 of the line with weight |x|2α. This paper is concerned primarily with the case . Multiplier operators are defined on these spaces by using the usual definition on a subspace that is shown to be dense in the space. The case is treated by duality; is briefly treated using a recent result on fractional integrals. The periodic case is also sketched. 相似文献
8.
Let be a strongly equicontinuous Boolean algebra of projections on the quasi-complete locally convex space X and assume that the space L(X) of continuous linear operators on X is sequentially complete for the strong operator topology. Methods of integration with respect to spectral measures are used to show that the closed algebra generated by in L(X) consists precisely of those continuous linear operators on X which leave invariant each closed -invariant subspace of X. 相似文献
9.
Chandler Davis 《Linear algebra and its applications》1977,18(1):33-43
Problem: Given operators Aj ? O on Hilbert space , with ΣAj = 1, to find commuting projectors Ej on a Hilbert space ? such that (for all j) x1Ajy = x1Ejy for, x, y ∈ . This paper gives an explicit construction, quite different from the familiar solution. 相似文献
10.
We discuss here representation and Fredholm theory for C1-algebras generated by commuting isometries. More particularly, for n commuting isometries {Vj: 1 ? j ? n} on separable Hilbert space we give a representation resembling the well-known representation for a single isometry. Our representation permits an analysis of the C1-algebras =(Vj:1?j?n) generated by the {Vj}. The commutator ideal in is identified precisely and, under certain additional hypotheses, the Fredholm operators in are also precisely determined. Finally, we obtain formulas in terms of topological data for the index of Fredholm operators in some interesting algebras of the type (Vj:1?j?n). 相似文献
11.
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
12.
Steven G. Krantz 《Journal of Functional Analysis》1979,34(3):456-471
It is known that a function on n which can be well approximated by polynomials, in the mean over Euclidean balls, is Lipschitz smooth in the usual sense. In this paper an analogous theorem is proved in which n is replaced by a set X, the averages over balls are replaced by a family of sublinear operators satisfying certain axioms, and the polynomials are replaced by a class of functions having certain regularity properties with respect to the averaging operators. Applications are given to function theory on domains in n, to nilpotent Lie groups, and to the classical Euclidean case. The first application provides a characterization of the duals of Hardy spaces on the ball in n. 相似文献
13.
New first-order conformally covariant differential operators Pk on spinor-k-forms, i.e., tensor products of contravariant spinors with k-forms, in an arbitrary n-dimensional pseudo-Riemannian spin manifold, are introduced. This provides a series of generalizations of the Dirac operator , in analogy with the series of generalizations (introduced by the author in [1]) of the Maxwell operator and the conformally covariant Laplacian on functions. In particular, new intertwining operators for representations of SU(2, 2) and SO(p + 1, q + 1) are found. Related nonlinear covariant operators are also introduced, and mixed nonlinear covariant systems are obtained by coupling to the Yang-Mills-Higgs-Dirac system in dimension 4. The spinor-form bundle is isomorphic with E(3) = E ? E ? E, where E is the spin bundle, and the Pk give a covariant operator on sections of E(3). This is generalized to a covariant operator on E(2l + 1). The relation of powers of these operators to higher-order covariant operators on lower spin bundles (analogous to the relation between and ) is discussed. 相似文献
14.
Let X be a complex Banach space and a domain in the complex plane. Let f: → X be an analytic function such that ∥f(ζ)∥ is constant as ζ ? . If X is the complex plane, then by the classical maximum modulus theorem f;(ζ) itself is constant on . This is not the case in general. In the paper we study the norm-constant analytic functions whose values are bounded linear operators over an uniformly convex complex Banach space or, in particular, over a complex Hilbert space. 相似文献
15.
A (stochastic) operator-theoretic approach leads to expresssions for inverses of linear and nonlinear stochastic operators—useful for the solution of linear or nonlinear stochastic differential equations. Operator equations are developed for inverses of linear or nonlinear stochastic operators. Series expressions are obtained which allow writing the solution y=?1x of the operator equation y=x. Special cases are studied in which may be linear or nonlinear, deterministic or stochastic in various combinations. 相似文献
16.
Richard C MacCamy 《Journal of Differential Equations》1974,16(2):373-393
We consider equations of the form, u(t) = ? ∝0tA(t ? τ)g(u(τ)) dτ + ?(t) (I) on a Hubert space . A(t) is a family of bounded, linear operators on while g is a transformation on g ? which can be nonlinear and unbounded. We give conditions on A and g which yield stability and asymptotic stability of solutions of (I). It is shown, in particular, that linear combinations with positive coefficients of the operators eMt and ?eMtsin Mt where M is a bounded, negative self-adjoint operator on satisfy these conditions. This is shown to yield stability results for differential equations of the form, , on . 相似文献
17.
Let (Ω, , μ) be a measure space, a separable Banach space, and 1 the space of all bounded conjugate linear functionals on . Let f be a weak1 summable positive B(1)-valued function defined on Ω. The existence of a separable Hilbert space , a weakly measurable B()-valued function Q satisfying the relation is proved. This result is used to define the Hilbert space L2,f of square integrable operator-valued functions with respect to f. It is shown that for B+(1)-valued measures, the concepts of weak1, weak, and strong countable additivity are all the same. Connections with stochastic processes are explained. 相似文献
18.
R.Grant Woods 《Topology and its Applications》1985,21(3):287-295
Let be a closed-hereditary topological property preserved by products. Call a space -regular if it is homeomorphic to a subspace of a product of spaces with . Suppose that each -regular space possesses a -regular compactification. It is well-known that each -regular space X is densely embedded in a unique space γscPX with such that if f: X → Y is continuous and Y has , then f extends continuously to γscPX. Call -pseudocompact if γscPX is compact.Associated with is another topological property #, possessing all the properties hypothesized for above, defined as follows: a -regular space X has # if each -pseudocompact closed subspace of X is compact. It is known that the -pseudocompact spaces coincide with the #-pseudocompact spaces, and that # is the largest closed-hereditary, productive property for which this is the case. In this paper we prove that if is not the property of being compact and -regular, then # is not simply generated; in other words, there does not exist a space E such that the spaces with # are precisely those spaces homeomorphic to closed subspaces of powers of E. 相似文献
19.
For a closed densely defined operator T on a complex Hilbert space and a spectral measure E for of countable multiplicity q defined on a σ-algebra over an arbitrary space Λ we give three conceptually differing but equivalent answers to the question asked in the title of the paper (Theorem 1.5). We then study the simplifications which accrue when T is continuous or when q = 1 (Sect. 4). With the aid of these results we obtain necessary and sufficient conditions for T to be the integral of the spectral measure of a given group of unitary operators parametrized over a locally compact abelian group Γ (Sect. 5). Applying this result to the Hilbert space of functions which are L2 with respect to Haar measure for Γ, we derive a generalization of Bochner's theorem on multiplication operators (Sect. 6). Some results on the multiplicity of indicator spectral measures over Γ are also obtained. When Γ = we easily deduce the classical theorem about the commutant of the associated self-adjoint operator (Sect. 7). 相似文献
20.
Barry Simon 《Journal of Functional Analysis》1981,42(3):347-355
We consider Schrödinger operators for a large class of potentials. V. We show that if H? = E? has a polynomially bounded solution ? then E is in the spectrum of H. This is accomplished by proving that the spectrum of H as an operator on L2 is identical to its spectrum as an operator on the weighted L2 space, L2δ. 相似文献