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1.
A Banach space operator satisfies “property (w)” if the complement of its essential Weyl approximate point spectrum in its approximate point spectrum is the set of finite multiplicity isolated eigenvalues of the operator. Property (w) does not transfer from operators A and B to their tensor product A?B; we give necessary and/or sufficient conditions ensuring the passage of property (w) from A and B to A?B. Perturbations by Riesz operators are considered.  相似文献   

2.
If (R,M) is a quasilocal integral domain of Krull dimension n,?1<n≤∞, and E is the direct sum of denumerably many copies of R/M, then T:=R?E is a reduced n-dimensional universal survival ring which is not a universal lying-over ring. In fact, T is a new kind of such ring, as T is not (isomorphic to) an A+B construction and T is not a ring of continuous real-valued functions. The analysis includes identifying all the prime ideals of T and showing that T is its own total quotient ring and satisfies Property A. The assertion would fail if n=1, as T would be a universal lying-over ring in this case. It is also shown that a (commutative unital) ring A satisfies Property A if and only if each ideal of A that consists only of zero-divisors survives in the complete ring of quotients of A.  相似文献   

3.
We consider weak solutions to the parabolic system ?u i?t?D α A i α (?u)=B i(?u) in (i=1,...,) (Q=Ω×(0,T), R n a domain), where the functionsB i may have a quadratic growth. Under the assumptionsn≤2 and ?u ?L loc 4+δ (Q; R nN ) (δ>0) we prove that ?u is locally Hölder continuous inQ.  相似文献   

4.
We prove that for an arbitrary setA ? ? its interior in aψ-density topology equalsA ∩ φβ(B), whereB is a measurable kernel ofA andβ is some countable ordinal. Moreover, eachβ, 1≤β<Ω, realizes the interior ofA for someA εS.  相似文献   

5.
Given a closed operatorA acting in a Banach spaceX, we define the regular (respectively the essentialy regular) spectrum σ r (A) (respectively σ e,r (A)) ofA. We prove that σ r (A) and σ e,r (A) are a closed subsets of the classical spectrum σ(A) ofA. Morever ifA is bounded we prove that σ r (A) and σ e,r (A)) satisfies the spectral mapping theorem.  相似文献   

6.
Let A and B be commutative locally convex algebras with unit. A is assumed to be a uniform topological algebra. Let Φ be an injective homomorphism from A to B. Under additional assumptions, we characterize the continuity of the homomorphism Φ?1/Im?Φ by the fact that the radical (or strong radical) of the closure of Im?Φ has only zero as a common point with Im?Φ. This gives an answer to a conjecture concerning some automatic continuity theorems on uniform topological algebras.  相似文献   

7.
In a locallyA-convex algebra (E, τ) we consider the associatedm-convex topologym(τ). We show that the completion ofE with respect tom(τ) is always a locallyA-convex algebra contained in the complete locally convex space obtained from (E, τ). The topologym(τ) is also used to characterize locally boundedly multiplicatively convex algebras among locallyA-convex ones.  相似文献   

8.
Let A be a commutative ring with unit and HA the set of formal expressions of the type \(f=\sum_{i:0}^{\infty}a_{i}X^{i}\) where a i A. When \(g=\sum_{i:0}^{\infty}b_{i}X^{i}\) then \(f+g=\sum_{i:0}^{\infty}(a_{i}+b_{i})X^{i}\) and \(f*g=\sum_{n:0}^{\infty}c_{n}X^{n}\) with \(c_{n}=\sum_{i:0}^{n}C_{n}^{i}a_{i}b_{n-i}\), where \(C_{n}^{i}={n!\over i!(n-i)!}\). With these two operations HA is a commutative ring with identity. It was introduced and studied by Keigher in 1997. In this note we continue the investigation and we focus on factorization in HA and its sub-ring hA of Hurwitz polynomials. We recall from Benhissi (Contrib. Algebra. Geom. 48(1):251–256, 2007, Proposition 1.1) and Keigher (Commun. Algebra 25(6):1845–1859, 1997, Corollary 2.8) that HA is an integral domain if and only if A is an integral domain with zero characteristic. Let π 0:HA?A be the natural ring homomorphism that assigns to each series its constant term. The key property is that a series fHA is a unit in HA if and only if π 0(f) is a unit in A, Keigher (Commun. Algebra 25(6):1845–1859, 1997, Proposition 2.5).  相似文献   

9.
LetA be a commutative Banach algebra with unit. Denote byX A, the global spectrum ofA. There is a holomorphic functional calculusθ A:O(X A)→A such thatθ A(â)=a. In this paper, we show the uniqueness of the global holomorphic functional calculus and we establish its compatibility with Banach algebra morphisms. We also extend this holomorphic functional calculus to the case ofImc algebras.  相似文献   

10.
LetR s be the subalgebra ofM 2(K[t]/(t s )) generated bye 11,e 22,te 12 andte 21, whereK is a field of characteristic 0,K[t] is the polynomial algebra in one variablet and (t s ) is the principal ideal inK[t], generated byt s . The main result of this paper is that we have described theT-idealT(R s ). Besides the two matrix polynomial identities — the standart identityS 4 and the identity of Hall, thisT-ideal is generated by one more explicitly given identity. The algebrasR s are interesting due to the fact that the proper identities of any subvarietyu of the variety ?=varM 2(K), generated by the matrix algebraM 2(K) of second order overK, asymptoticaly coincide with the proper identities of someR s .  相似文献   

11.
In this paper we study the hyperstructures, saidP-hypergroupoids, (H, P*) in whichH is a set andP* is one of the hyperoperations defined as follows: ?(x, y) εH 2,xP*y=xyP orxP*y=Pxy whereP is a subset ofH. In particular we give a general formula for to express the simple hyperproducts ofn elements and then we consider some cases in which (H, P*) is feebly associative. We study, in such cases theβ-relations.  相似文献   

12.
LetR be a prime ring andD a nonzero derivation ofR. If one of the four conditions holds inR, thenR is commutative:
  1. (i)
    X 2D(X)?D(X)X2∈Z(R), CharR≠2;  相似文献   

13.
In this paper we define the stochastic integral for two parameter processes with values in a Banach spaceE. We use a measure theoretic approach. To each two parameter processX withX st L E p we associate a measureI X with values inL E p . IfX isp-summable, i.e. ifI X can be extended to aσ-additive measure with finite semivariation on theσ-algebra of predictable sets, then the integralε HdI X can be defined and the stochastic integral is defined by (H·X) z =ε [0,z] HdI X . We prove that the processes with finite variation and the processes with finite semivariation are summable and their stochastic integral can be computed pathwise, as a Stieltjes Integral of a special type.  相似文献   

14.
We use extreme point methods to obtain some existence theorems for invariant and hyperinvariant subspaces for certain classes of operators In Hilbert space. These convexity methods have, heretofore, not been used in this context, however it would appear that they provide useful alternatives to existing methods. Using the Krein-Milman theorem we prove several variants of the classical lemma of I. Schur. In one of the main results we prove the following: LetAB (H), thenA andA* have a common non-trivial closed hyperinvariant subspace if and only if there exists a non-scalar operatorW εB(H) such that bothW andW* belong to the double commutant ofA.  相似文献   

15.
We consider a class of hyperbolic 3-orbifoldsO(α/β); the underlying topological space of such an orbifold is the 3-sphere and the singular set is obtained by adding the two standard (upper and lower) unknotting tunnels to a 2-bridge linkL(α/β) (and associating branching order two to both unknotting tunnels). These 3-orbifolds are extremal with respect to the notion of Heegaard genus or Heegaard number of 3-orbifolds; it is to be expected that they are also extremal with respect to the volume, that is the smallest volume hyperbolic 3-orbifolds should belong to this or some closely related class. We show that an orbifoldO(α/β) has a uniqueD 2-covering by an orbifold? n(α/β) wose space is the 3-sphere and whose singular set is the same 2-bridge linkL(α/β) used for the construction ofO(α/β); moreoverO(α/β) is hyperbolic if and only if? n(α/β) is hyperbolic. As the volumes of the orbifolds? n(α/β) are known resp. can be computed, this allows to compute the volumes of the orbifoldsO(α/β). The problem of computation of volumes remains open for some closely related classes of 3-orbifolds which are also extremal with respect to the Heegaard genus (for example associating a branching order bigger than two to one or both unknotting tunnels).  相似文献   

16.
We generalize the notion of a spectral state (as introduced for Banach algebras by Moore, Bonsall and Duncan) to the context of locally multiplicatively-convex (LMC) algebras by proceeding in a way analogous to the generalization of numerical range theory from Banach algebras toLMC-algebras carried out by Giles and Koehler. Among the results obtained in this note are integral representations of spectral states by probability measures on the structure space ofA and the determination of the extreme points of the convex set\(\Omega _A \) of all spectral states on a commutativeLMC-algebraA (which is related to different Choquet boundaries) as well as a characterization of symmetric involutions by the coincidence of the notions of positive state and spectral state and a characterization of theQ-property by the weak-*-boundedness of\(\Omega _A \). The paper finishes with two elementary commutativity criteria involving spectral states and two Korovkin-type theorems for the approximation of unital algebra homomorphisms by σ-equicontractive nets of linear operators mapping anLMC-algebraA into theLMC-algebra of all continuous complex-valued functions on a completely regular spaceX.  相似文献   

17.
SianoR un anello primo di caratteristica differente da 2,d una derivazione non nulla diR, L un ideale di Lie non centrale diR, a ∈ R. Sea[d(u), u] = 0, per ogni scelta diu ∈ L, alloraa = 0.  相似文献   

18.
It is proved that a setH inR n has Lebesgue null measure if any function which is the restriction toH of a Baire function defined inR n is the restriction toH of a derivative of an interval function.  相似文献   

19.
In this paper we consider some questions concerning unitary spaces (V, h), even though (V, h) is not finitely generated. Our main result is as follows: letF be an infinite field of characteristic ≠2 andD anm 2-dimensional central division algebra overF with an involutionj≠1. Let Σj(D) denote the subgroup of the multiplicative groupD * generated by the non zero symmetric elements. If (V, h) is an infinite dimensional regular unitary space of Witt index at least two overD, then the finitary unitary groupFU(h) is a simple group if and only ifD*=Σj(D)[D*, D*]. On the other hand, when (V, h) is not regular,FU(h) cannot be simple since it containsFU 0(h), the subgroup of elements ofFU(h) acting trivially onrad(V, h), as a normal subgroup. In the non regular case we show that under the above assumptions evenFU 0(h) is not a simple group.  相似文献   

20.
We present an algorithm to compute the number ofF q -rational points on elliptic curves defined over a finite fieldF q , withj-invariant 0 or 1728. This algorithm takesO(log3 p) bit operations, werep is the characteristic ofF q .  相似文献   

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