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1.
For an arbitrary set E and a given closure operator , we want to construct a symmetric closure operator via some – possibly infinite – iteration process. If E is finite, the corresponding symmetric closure operator . defines a matroid. If and is the convex closure operator, turns out to be the affine closure operator. Moreover, we apply the symmetrization process to closure operators induced by visibility. Received March 9, 2005  相似文献   

2.
We study sums of bisectorial operators on a Banach space X and show that interpolation spaces between X and D(A) (resp. D(B)) are maximal regularity spaces for the problem Ay + By = x in X. This is applied to the study of regularity properties of the evolution equation u′ + Au = f on for or and the evolution equation u′ + Au = f on [0, 2π] with periodic boundary condition u(0) = u(2π) in or   相似文献   

3.
Let be a symmetric operator with compact resolvent defined in a Hilbert space For any fixed we consider an entire function Ka which involves the resolvent of Associated with Ka we obtain, by duality in a Hilbert space of entire functions which becomes a De Branges space of entire functions. This property provides a characterization of regardless of the anti-linear mapping which has as its range space. There exists also a sampling formula allowing to recover any function in from its samples at the sequence of eigenvalues of This work has been supported by the grant BFM2003–01034 from the D.G.I. of the Spanish Ministerio de Ciencia y Tecnología.  相似文献   

4.
Properties of several sorts of lattices of convex subsets of are examined. The lattice of convex sets containing the origin turns out, for n > 1, to satisfy a set of identities strictly between those of the lattice of all convex subsets of and the lattice of all convex subsets of The lattices of arbitrary, of open bounded, and of compact convex sets in all satisfy the same identities, but the last of these is join-semidistributive, while for n > 1 the first two are not. The lattice of relatively convex subsets of a fixed set satisfies some, but in general not all of the identities of the lattice of “genuine” convex subsets of To the memory of Ivan RivalReceived April 22, 2003; accepted in final form February 16, 2005.This revised version was published online in August 2005 with a corrected cover date.  相似文献   

5.
We show that for a variety of Heyting algebras the following conditions are equivalent: (1) is locally finite; (2) the -coproduct of any two finite -algebras is finite; (3) either coincides with the variety of Boolean algebras or finite -copowers of the three element chain are finite. We also show that a variety of Heyting algebras is generated by its finite members if, and only if, is generated by a locally finite -algebra. Finally, to the two existing criteria for varieties of Heyting algebras to be finitely generated we add the following one: is finitely generated if, and only if, is residually finite. Received November 11, 2001; accepted in final form July 25, 2005.  相似文献   

6.
It is shown that for open convex , d > 1 and a nontrivial polynomial P the space does not have property . If P is elliptic or homogeneous, then this holds for every open Ω. For even cannot occur and if it occurs for some Ω, then P must be hypoelliptic. Received: 18 July 2005  相似文献   

7.
We establish a symbol calculus for the C*-subalgebra of generated by the operators of multiplication by slowly oscillating and piecewise continuous functions and the operators where is the Cauchy singular integral operator and The C*-algebra is invariant under the transformations
where Uz is the rotation operator Using the localtrajectory method, which is a natural generalization of the Allan-Douglas local principle to nonlocal type operators, we construct symbol calculi and establish Fredholm criteria for the C*-algebra generated by the operators and for the C*-algebra generated by the operators and and for the C*-algebra generated by the algebras and The C*-algebra can be considered as an algebra of convolution type operators with piecewise slowly oscillating coefficients and shifts acting freely.  相似文献   

8.
It is known that if and are Banach space operators with the single-valued extension property, SVEP, then the matrix operator has SVEP for every operator and hence obeys Browder’s theorem. This paper considers conditions on operators A, B, and M0 ensuring Weyls theorem for operators MC.  相似文献   

9.
Let be a group of affine transformations of the Euclidean plane . Two topological discs D, are called congruent by dissection with respect to if D can be dissected into a finite number of subdiscs that can be rearranged by maps from to a dissection of E. Our main result says in particular that admits congruence by dissection of any circular disc C with any square S if and only if contains a contractive map and all orbits , , are dense in . In this case any two discs D and E are congruent by dissection with respect to and every disc D is congruent by dissection with n copies of D for every n ≥ 2. Moreover, we give estimates on minimal numbers of pieces that are needed to realize congruences by dissection. Dedicated to Irmtraud Stephani on the occasion of her 70th birthday  相似文献   

10.
An Ockham algebra that satisfies the identity is called a Kn, m-algebra. Generalizing some results obtained in [2], J. Varlet and T. Blyth, in [3, Chapter 8], study congruences on K1, 1-algebras. In particular, they describe the complement (when it exists) of a principal congruence and characterize these congruences that are complemented. In this paper we study the same question for Kn, m-algebras. Received March 24, 2005; accepted in final form April 28, 2005.  相似文献   

11.
In the present paper we suggest an explicit construction of a Cartan connection for an elliptic or hyperbolic CR manifold M of dimension six and codimension two, i.e. a pair , consisting of a principal bundle over M and of a Cartan connection form over P, satisfying the following property: the (local) CR transformations are in one to one correspondence with the (local) automorphisms for which . For any , this construction determines an explicit monomorphism of the stability subalgebra Lie (Aut(M)x) into the Lie algebra of the structure group H of P. Mathematics Subject Classification (2000) Primary 32V05, Secondary 53C15, 53A55  相似文献   

12.
Let L and M be Archimedean vector lattices such that and are complex vector lattices. We constructively and intrinsically prove that if is an order bounded disjointness preserving operator from into then the modulus
of exists in the ordered vector space of all order bounded operators from L into M. Received February 11, 2005; accepted in final form March 8, 2005.  相似文献   

13.
Let be a homogeneous Noetherian ring with local base ring (R0,m0) and let M,N be two finitely generated graded R-modules. Let denote the i-th graded generalized local cohomology of N relative to M with support in . We study the vanishing, tameness and asymptotical stability of the homogeneous components of . Received: 22 March 2005; revised: 25 June 2005  相似文献   

14.
Let p be a prime, a finite p-group, any finite group with order divisible by p, and any action of on . We show that the cardinality of the set of all derivations with respect to this action is a multiple of p. This generalises theorems of Frobenius and Hall. Received: 16 June 2003  相似文献   

15.
We show that if A is a separable, nuclear, -absorbing (or strongly purely infinite) C*-algebra which is homotopic to zero in an ideal-system preserving way, then A is the inductive limit of C*-algebras of the form where Γ is a finite connected graph (and is the algebra of continuous functions on Γ that vanish at a distinguished point ).We show further that if B is any separable, nuclear C*-algebra, then is isomorphic to a crossed product where D is an inductive limit of C*-algebras of the form (and D is -absorbing and homotopic to zero in an ideal-system preserving way).Received: December 2003 Revision: July 2004 Accepted: July 2004  相似文献   

16.
Let X, Y be Banach spaces. We say that a set is uniformly p–summing if the series is uniformly convergent for whenever (xn) belongs to . We consider uniformly summing sets of operators defined on a -space and prove, in case X does not contain a copy of c0, that is uniformly summing iff is, where Tx) = (T#φ) x for all and xX. We also characterize the sets with the property that is uniformly summing viewed in . Received: 1 July 2005  相似文献   

17.
Birkhoff coordinates for KdV on phase spaces of distributions   总被引:1,自引:0,他引:1  
The purpose of this paper is to extend the construction of Birkhoff coordinates for the KdV equation from the phase space of square integrable 1-periodic functions with mean value zero to the phase space of mean value zero distributions from the Sobolev space endowed with the symplectic structure More precisely, we construct a globally defined real-analytic symplectomorphism where is a weighted Hilbert space of sequences supplied with the canonical Poisson structure so that the KdV Hamiltonian for potentials in is a function of the actions alone.  相似文献   

18.
Let R be a unital associative ring and two classes of left R-modules. In this paper we introduce the notion of a In analogy to classical cotorsion pairs as defined by Salce [10], a pair of subclasses and is called a if it is maximal with respect to the classes and the condition for all and Basic properties of are stated and several examples in the category of abelian groups are studied. Received: 17 March 2005  相似文献   

19.
For Banach space operators T satisfying the Tadmor-Ritt condition a band limited H calculus is established, where and a is at most of the order C(T)5. It follows that such a T allows a bounded Besov algebra B∞ 10 functional calculus, These estimates are sharp in a convenient sense. Relevant embedding theorems for B∞ 10 are derived. Received: 25 October 2004; revised: 31 January 2005  相似文献   

20.
We consider two pairs of complete hereditary cotorsion theories on the category of left R-modules, such that We prove that for any left R-modules M, N and for any n ≧ 1, the generalized Tate cohomology modules can be computed either using a left of M and a left of M or using a right a right of N. Received: 17 December 2004  相似文献   

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