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1.
The main purpose of this paper is to study spectral and B-Fredholm properties of a multiplierT acting on a semi-simple regular tauberian commutative Banach algebraA. We show thatT is a B-Fredholm operator if and only ifT is a semi B-Fredholm operator, and in this case we have the indexind(T)=0. Moreover we give some spectral properties for multipliers. Spectral mapping theorems for the Weyl’s and B-Weyl spectrum
of a multiplier are also considered. Furthermore we show that Weyl’s theorem and generalized Weyl’s theorem hold for a multiplierT. Finally we give sufficient conditions for a multiplier to be a product of an invertible and an idempotent operators. 相似文献
2.
If T is an orthomodular lattice (OML), we denote by [T] the equational class generated by T. In this paper we characterize the finite OMLs T such that [T] covers some [MO
n
]. These OMLs T are the non-modular OMLs such that all proper sub-OMLs of T are modular. An OML satisfying that last property is called minimal. There exist infinitely many minimal OMLs provided by
quadratic spaces over finite fields. We describe them and give a new way to represent their Greechie diagrams in two separate
parts. Other methods to obtain finite minimal OMLs are given.
Received May 14, 2005; accepted in final form May 30, 2007. 相似文献
3.
Azeeza Ali Ismaeel 《Semigroup Forum》1994,48(1):193-196
We give a characterization of theE-unitary covers for a Bruck semigroup, which is a generalization of Theorem 3 given in [1].
In a recent paper [1] we gave a characterization of theE-unitary covers for a Bruck semigroupB(T,α) whereT is a finite chain of groups, and now we give a characterization forB(T,α) whereT is any inverse semigroup.
We use here the notations and the terminology of Petrich's book [2].
First we prove a Theorem which is more general than [[1], Theorem 2].
I wish to express my thanks to Dr. G. Pollák for his valuable advice. 相似文献
4.
5.
David L. Wehlau 《manuscripta mathematica》1994,82(1):161-170
Let ρ:T→GL(V) be a finite dimensional rational representation of a torus over an algebraically closed fieldk. We give necessary and sufficient conditions on the arrangement of the weights ofV within the character lattice ofT for the ring of invariants,k[V]
T
, to have a homogeneous system of parameters consisting of monomials (Theorem 4.1). Using this we give two simple constructive
criteria each of which gives necessary and sufficient conditions fork[V]
T
to be a polynomial ring (Theorem 5.8 and Theorem 5.10).
Research supported in part by NSERC Grant OGP 137522 相似文献
6.
Given a skew product flow (T,T
2) on the two torus, we construct a family of flows onT
3 parametrized by elements of the circleT. We show that under a certain condition on (T,T
2) almost every flow in this family is strictly ergodic. This is used to characterize minimal subsets of the flow (T,P(T
2)) induced byT on the space of probability measures onT
2. Using a result of M. Herman, we give an example to show that this characterization does not hold for everyT.
To the memory of Shlomo Horowitz 相似文献
7.
1.IntroductionWeshallassumefamiliaritywithmatroidtheory--foranintroduction,andforthedefinitionoftermsnotdefinedinthispaper,see[31.Edmonds'matroidpartitiontheoremisaveryimportanttheorem,whichhasmanyapplications.Twoclassicresultsof[4,5],whichconcernwithpackingandcoveringoftheedgesetofagraphwithkedge--disjointspanningtrees,canbeeasilydeducedfromit(see[3],PP.125--127).Inthepresentpaperwewillpresentamatroidapproachtotheproblemoftreedecompositionraisedrecently(see[6,7]).Ourmainaimistogivealternati… 相似文献
8.
We give a sufficient condition for the validity of the implication limn→∞ Tnx=0⇒∑∞n=0Tnxconverges, whereT:X→Xis a bounded linear operator,Xis a Banach space, andx∈X. From this condition we derive the results given by other authors. Moreover, we give some properties about the operators that verifies the above implication, which are called Neumann operators. 相似文献
9.
Mohan Joshi 《Proceedings Mathematical Sciences》1980,89(2):95-100
Let (Ω,B,μ) be ameasure space andX a separable Hubert space. LetT be a random operator from Ω ×X intoX. In this paper we investigate the measurability ofT
-1. In our main theorems we show that ifT is a separable random operator withT(w) almost sure invertible and monotone and demicontinuous thenT
-1is also a random operator. As an application of this we give an existence theorem for random Hammerstein operator equation. 相似文献
10.
11.
In this paper we give a graphical method which can be used to determine whether or not a group presentation satisfies the
small cancellation conditionT(q). We use this method to determine all 2- and 3-generator presentations satisfyingT(4). 相似文献
12.
Theo De Jong 《Compositio Mathematica》1998,113(1):67-90
In this paper we give explicit equations for determinantal rational surface singularities and prove dimension formulas for the T
1 and T
2 for those singularities. 相似文献
13.
In this paper, We give an equivalent condition between Poincaré inequality and T
2-transportation inequality, and by this result we find a series of measures to enhance the claim that Log-Sobolev inequality
is stronger than T
2-transportation cost inequality. 相似文献
14.
Mme F. Chatelin 《Numerische Mathematik》1973,20(3):193-204
To be computed, the eigenvalues of a closed linear operatorT in a Banach space are usually approximated by the eigenvalues ofT
h, a linear operator approximatingT in a finite dimensional space (for example, finite difference method, Galerkin method),h is a parameter which tends to 0. This approximation is studied in [2]; stability ofT
h implies the continuity of the spectrum ofT
h, whenh tends to 0.We present here a new kind of sufficient condition. For that purpose, we disconnect the continuity of the spectrum ofT
h into lower and upper semicontinuities. And we give two different criteria for these semi-continuities. Applications to the approximation of nonselfadjoint elliptic operators by finite difference schemes, are given. 相似文献
15.
Let T be a Banach space operator, E(T) be the set of all isolated eigenvalues of T and π(T) be the set of all poles of T. In this work, we show that Browder's theorem for T is equivalent to the localized single-valued extension property at all complex numbers λ in the complement of the Weyl spectrum of T, and we give some characterization of Weyl's theorem for operator satisfying E(T) = π(T). An application is also given. 相似文献
16.
R. Penne 《Discrete and Computational Geometry》1996,15(1):15-33
We study line configurations in 3-space by means of “line diagrams”, projections into a plane with an indication of over and
under crossing at the vertices. If we orient such a diagram, we can associate a “contracted tensor”T with it in the same spirit as is done in Knot Theory. We give conditions to makeT independent of the orientation, and invariant under isotopy. The Yang-Baxter equation is one such condition. Afterwards we
restrict ourselves to Yang-Baxter invariants with a topological state model, and give some new invariants for line isotopy. 相似文献
17.
Yasunori Ishibashi 《代数通讯》2013,41(3):575-584
Let R be an associative ring with 1 and let T be a hereditary torsion theory in the category of left R-modules. In defining the localizatio n of R respect to x, the concept of T-injective module arises (see [5] , [11]) . We can consider the family E T of all short exact sequences of left R-modules respect to which every T-injective left R-module is injective . E T proper class in the sense defined in [ 9] . In this paper we characterize proper classe s which are of the form E T for some hereditary torsion theory x. On the other hand, we give some conditions on x, which imply that E T has enough projectives , and we show an example where E T does not have enough projectives. 相似文献
18.
We study the approximation of a continuous function field over a compact set T by a continuous field of ridge approximants over T, named ridge function fields. We first give general density results about function fields and show how they apply to ridge function fields. We next discuss the parameterization of sets of ridge function fields and give additional density results for a class of continuous ridge function fields that admits a weak parameterization. Finally, we discuss the construction of the elements in that class. 相似文献
19.
In this note we provide regularity conditions of closedness type which guarantee some surjectivity results concerning the
sum of two maximal monotone operators by using representative functions. The first regularity condition we give guarantees
the surjectivity of the monotone operator S(· + p) + T(·), where p ɛ X and S and T are maximal monotone operators on the reflexive Banach space X. Then, this is used to obtain sufficient conditions for the surjectivity of S + T and for the situation when 0 belongs to the range of S + T. Several special cases are discussed, some of them delivering interesting byproducts. 相似文献
20.
A bounded linear operator T ∈ L(X) on aBanach space X is said to satisfy “Browder’s theorem” if the Browder spectrum coincides with the Weyl spectrum. T ∈ L(X) is said to satisfy “a-Browder’s theorem” if the upper semi-Browder spectrum coincides with the approximate point Weyl spectrum. In this note we give several characterizations of operators satisfying these theorems. Most of these characterizations are obtained by using a localized version of the single-valued extension property of T. In the last part we shall give some characterizations of operators for which “Weyl’s theorem” holds. 相似文献