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991.
James L. Heitsch 《K-Theory》1995,9(6):507-528
In this paper, we show how to define a Bismut superconnection for generalized Dirac operators defined along the leaves of a compact foliated manifoldM. Using the heat operator of the curvature of the superconnection, we define a (nonnormalized) Chern character for the Dirac operator, which lies in the Haefliger cohomology of the foliation. Rescaling the metric onM by 1/a and lettinga 0, we obtain the analog of the classical cohomological formula for the index of a family of Dirac operators. In certain special cases, we can also compute the limit asa and show that it is the Chern character of the index bundle given by the kernel of the Dirac operator. Finally, we discuss the relation of our results with the Chern character in cyclic cohomology.  相似文献   
992.
Normality preserving multiplication operators   总被引:1,自引:0,他引:1  
We show that a multiplication operator (T)=ATB is normality preserving if and only if it is hyponormality preserving, if and only if it is either of the formA=fg,B=h f, orA=D,B=D* for someC andD* D=I. Also we show that is (semi-) Fredholmness prserving if and only ifA andB are (semi-) Fredholm operators.Supported by the Science Foundation of Zhejiang Province and NSF.  相似文献   
993.
If Au = - div(a(x, Du)) is a monotone operator defined on the Sobolev space W1,P(R n, 1 < p < + , with a(x,0) = 0 for a.e. x Rn, the capacity C_A(E,F) relative to A can be defined for every pair (E,F) of bounded sets in Rn with E F. The main properties of the set function CA(E,F) are investigated. In particular it is proved that CA(E,F) is increasing and countably subadditive with respect to E, decreasing with respect to F, and continuous, in a suitable sense, with respect to E and F.  相似文献   
994.
In this paper an easier proof is obtained of Alexandru Aleman's extension of an inequality of Axler and Shapiro for subnormal operators to the essential norm. The method is applied to show that a hyponormal operator whose essential spectrum has area zero must be essentially normal.

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995.
It is proved that if a generalized Goursat-Darboux problem is -well posed then the operator cannot contain derivatives with respect to one of the variables.

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996.
Let be a rearrangement invariant space, an arbitrary set and a von Neumann algebra with a semifinite normal faithful trace. It is proved that the associated symmetric space of measurable operators has -RNP if and only if has -RNP extending in this way some previous results by Q. Xu.

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997.
The concept of quasispectral maximal subspaces for quasinilpotent (but not nilpotent) operators was introduced by M. Omladi\v{c} in 1984. As an application a class of quasinilpotent operators on -spaces, close to the Volterra kernel operator, was studied. In the present Banach function space setting we determine all quasispectral maximal subspaces of analogues of such operators and prove that these subspaces are all the invariant bands. An example is given showing that (in general) they are not all the closed, invariant ideals of the operator.

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998.
We show that if is a separable symmetric Banach function space on the positive half-line, then has the Kadec-Klee property (respectively, uniform Kadec-Klee property) for local convergence in measure if and only if, for every semifinite von Neumann algebra , the associated space of -measurable operators has the same property.

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999.
We show that even in the case of a Banach lattice with an order continuous norm (or whose dual has an order continuous norm) the linear span of the positive compact operators on need not be complete under the regular norm.

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1000.
Weak type bounds for a class of rough operators with power weights   总被引:6,自引:0,他引:6  
In this note we show that and the fractional integral and maximal operators with rough kernel respectively, are bounded operators from to where and

  相似文献   

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