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1.
Let M be a type I von Neumann algebra with the center Z, and a faithful normal semi-finite trace τ. Consider the algebra L(M, τ) of all τ-measurable operators with respect to M and let S
0(M, τ) be the subalgebra of τ-compact operators in L(M, τ). We prove that any Z-linear derivation of S
0(M, τ) is spatial and generated by an element from L(M, τ).
相似文献
2.
In the present paper we consider a von Neumann algebra M with a faithful normal semi-finite trace τ, and {α
t
}, a strongly continuous extension to L
p
(M, τ) of a semigroup of absolute contractions on L
1(M, τ). By means of a non-commutative Banach Principle we prove for a Besicovitch function b and x ∊ L
p
(M, τ), that the averages 1/T ∫0
T
b(t)α
t
(x)dt converge bilateral almost uniformly in L
p
(M, τ) as T → 0.
Communicated by Dénes Petz 相似文献
3.
Let L(H) denote the algebra of all bounded linear operators on a separable infinite dimensional complex Hilbert space H into itself. Given A ∈ L(H), we define the elementary operator Δ
A
: L(H) → L(H) by Δ
A
(X) = AXA − X. In this paper we study the class of operators A ∈ L(H) which have the following property: ATA = T implies AT*A = T* for all trace class operators T ∈ C
1(H). Such operators are termed generalized quasi-adjoints. The main result is the equivalence between this character and the
fact that the ultraweak closure of the range of Δ
A
is closed under taking adjoints. We give a characterization and some basic results concerning generalized quasi-adjoints
operators. 相似文献
4.
Let be a nilpotent connected and simply connected Lie group, and an analytic subgroup of G. Let , be a unitary character of H and let . Suppose that the multiplicities of all the irreducible components of τ are finite. Corwin and Greenleaf conjectured that
the algebra of the differential operators on the Schwartz-space of τ which commute with τ is isomorphic to the algebra of H-invariant polynomials on the affine space . We prove in this paper this conjecture under the condition that there exists a subalgebra which polarizes all generic elements
in . We prove also that if is an ideal of , then the finite multiplicities of τ is equivalent to the fact that the algebra is commutative. 相似文献
5.
Let L be a Lie algebra with universal enveloping algebra U(L). We prove that if H is another Lie algebra with the property that U(L) ≅ U(H) then certain invariants of L are inherited by H. For example, we prove that if L is nilpotent then H is nilpotent with the same class as L. We also prove that if L is nilpotent of class at most two then L is isomorphic to H.
Presented by D. Passman 相似文献
6.
Let be a nilpotent connected and simply connected Lie group, and an analytic subgroup of G. Let , be a unitary character of H and let . Suppose that the multiplicities of all the irreducible components of τ are finite. Corwin and Greenleaf conjectured that
the algebra of the differential operators on the Schwartz-space of τ which commute with τ is isomorphic to the algebra of H-invariant polynomials on the affine space . We prove in this paper this conjecture under the condition that there exists a subalgebra which polarizes all generic elements
in . We prove also that if is an ideal of , then the finite multiplicities of τ is equivalent to the fact that the algebra is commutative.
(Received 15 November 2000) 相似文献
7.
8.
AliGhaffari AlirezaMedghalchi 《数学学报(英文版)》2004,20(2):201-208
For a locally compact group G, L^1 (G) is its group algebra and L^∞(G) is the dual of L^1 (G).Lau has studied the bounded linear operators T:L^∞(G)→L^∞(G) which commute with convolutions and translations. For a subspace H of L^∞(G), we know that M(L^∞(G),H), the Banach algebra of all bounded linear operators on L^∞(G) into H which commute with convolutions, has been studied by Pyre and Lau. In this paper, we generalize these problems to L(K)^*, the dual of a hypergroup algebra L(K) in a very general setting, i.e. we do not assume that K admits a Haar measure. It should be noted that these algebras include not only the group algebra L^1(G) but also most of the semigroup algebras.Compact hypergroups have a Haar measure, however, in general it is not known that every hypergroup has a Haar measure. The lack of the Haar measure and involution presents many difficulties; however,we succeed in getting some interesting results. 相似文献
9.
In this paper we consider traces on a von Neumann algebra M with values in complex Kantorovich-Pinsker spaces. We establish the connection between the convergence with respect to the
trace and the convergence locally in measure in the algebra S(M) of measurable operators affiliated with M. We define the (bo)-complete lattice-normed spaces of integrable operators in S(M) and prove that they are decomposable if the trace possesses the Maharam property. 相似文献
10.
We prove an operator space version of Maurey’s theorem, which claims that every absolutely (p, 1)-summing map on C(K) is automatically absolutely q-summing for q > p. Our results imply in particular that every completely bounded map from B(H) with values in Pisier’s operator space OH is completely p-summing for p > 2. This fails for p = 2. As applications, we obtain eigenvalue estimates for translation invariant maps defined on the von Neumann algebra V
N(G) associated with a discrete group G. We also develop a notion of cotype which is compatible with factorization results on noncommutative L
p
spaces. 相似文献
11.
We first prove two forms of von Neumann’s mean ergodic theorems under the framework of complete random inner product modules.
As applications, we obtain two conditional mean ergodic convergence theorems for random isometric operators which are defined
on L
ℱ
p
(ℰ, H) and generated by measure-preserving transformations on Ω, where H is a Hilbert space, L
p
(ℰ, H) (1 ⩽ p < ∞) the Banach space of equivalence classes of H-valued p-integrable random variables defined on a probability space (Ω, ℰ, P), F a sub σ-algebra of ℰ, and L
ℱ
p
(ℰ(E,H) the complete random normed module generated by L
p
(ℰ, H). 相似文献
12.
Boundedness of maximal operators and potential operators on Carleson curves in Lebesgue spaces with variable exponent 总被引:1,自引:0,他引:1
We prove the boundedness of the maximal operator Mr in the spaces L^p(·)(Г,p) with variable exponent p(t) and power weight p on an arbitrary Carleson curve under the assumption that p(t) satisfies the log-condition on Г. We prove also weighted Sobolev type L^p(·)(Г, p) → L^q(·)(Г, p)-theorem for potential operators on Carleson curves. 相似文献
13.
14.
Let D be a bounded homogeneous domain in ℂ
n
. In this paper, we study the bounded and the compact weighted composition operators mapping the Hardy space H
∞(D) into the Bloch space of D. We characterize the bounded weighted composition operators, provide operator norm estimates, and give sufficient conditions
for compactness. We prove that these conditions are necessary in the case of the unit ball and the polydisk. We then show
that if D is a bounded symmetric domain, the bounded multiplication operators from H
∞(D) to the Bloch space of D are the operators whose symbol is bounded. 相似文献
15.
Albo Carlos Cavalheiro 《Applications of Mathematics》2006,51(6):619-628
In the paper we study the equation L
u
= f, where L is a degenerate elliptic operator, with Neumann boundary condition in a bounded open set μ. We prove existence and uniqueness
of solutions in the space H(μ) for the Neumann problem. 相似文献
16.
We consider the Cauchy problem of Navier-Stokes equations in weak Morrey spaces. We first define a class of weak Morrey type spaces Mp*,λ(Rn) on the basis of Lorentz space Lp,∞ = Lp*(Rn)(in particular, Mp*,0(Rn) = Lp,∞, if p > 1), and study some fundamental properties of them; Second,bounded linear operators on weak Morrey spaces, and establish the bilinear estimate in weak Morrey spaces. Finally, by means of Kato's method and the contraction mapping principle, we prove that the Cauchy problem of Navier-Stokes equations in weak Morrey spaces Mp*,λ(Rn) (1<p≤n) is time-global well-posed, provided that the initial data are sufficiently small. Moreover, we also obtain the existence and uniqueness of the self-similar solution for Navier-Stokes equations in these spaces, because the weak Morrey space Mp*,n-p(Rn) can admit the singular initial data with a self-similar structure. Hence this paper generalizes Kato's results. 相似文献
17.
Narcisse Randrianantoanina 《Journal of Functional Analysis》2010,258(11):3801-3817
We prove that if H is a Hilbert space then the Schatten (trace) class operators on H has the weak∗ fixed point property for left reversible semigroups. This answered positively a problem raised by A.T.-M. Lau. We also prove that if M is a finite von Neumann algebra then any nonempty bounded convex subset of the non-commutative L1-space associated to M that is compact for the measure topology has the fixed point property for left reversible semigroups. 相似文献
18.
Ferenc Weisz 《逼近论及其应用》2000,16(1):52-65
The two-dimensional classical Hardy space Hp(T×T) on the bidisc are introduced, and it is shown that the maximal operator of the (C,α,β) means of a distribution is bounded from the space Hp(T×T) to Lp(T2) (1/(α+1), 1/(β+1)<p≤∞), and is of weak type (H 1 # (T×T), L1(T2)), where the Hardy space H 1 # (T×T) is defined by the hybrid maximal function. As a consequence we obtain that the (C, α, β) means of a function f∈H 1 # (T×T)⊃LlogL(T 2) convergs a. e. to the function in question. Moreover, we prove that the (C, α, β) means are uniformly bounded on the spaces Hp(T×T) whenever 1/(α+1), 1(β+1)<p<∞. Thus, in case f∈Hp(T×T), the (C, α, β) means convergs to f in Hp(T×T) norm whenever (1/(α+1), 1/(β+1)<p<∞). The same results are proved for the conjugate (C, α, β) means, too. 相似文献
19.
CHEN Zhuo & LIU Zhangju Department of Mathematics Capital Normal University Beijing China School of Mathematical Science Peking University Beijing China 《中国科学A辑(英文版)》2006,49(2):277-288
For a transitive Lie algebroid A on a connected manifold M and its representation on a vector bundle F, we define a morphism of cohomology groups rk: Hk(A,F) → Hk(Lx,Fx), called the localization map, where Lx is the adjoint algebra at x ∈ M. The main result in this paper is that if M is simply connected, or H (LX,FX) is trivial, then T is injective. This means that the Lie algebroid 1-cohomology is totally determined by the 1-cohomology of its adjoint Lie algebra in the above two cases. 相似文献
20.
The aim of this work is to investigate the integrability properties of the maximal operator Mu,associated with a non-doubling measure μ defined on Rn. We start by establishing for a wide class of radial and increasing measures μ that Mu is bounded on all the spaces Lu^p(R^n),P〉1.Also,we show that there is a radial and increasing measure p for which Mμ does not map Lμ^p(R^n) into weak Lμ^p(R^n),1≤p〈∞. 相似文献