共查询到20条相似文献,搜索用时 31 毫秒
1.
《Quaestiones Mathematicae》2013,36(8):1079-1090
AbstractFor any ideal of closed sets in X, let be the family of those functions in C(X) whose support lie on . Further let contain precisely those functions f in C(X) for which for each ? > 0, {x ∈ X: |f (x)| ≥ ?} is a member of . Let stand for the set of all those points p in βX at which the stone extension f? for each f in is real valued. We show that each realcompact space lying between X and βX is of the form if and only if X is pseudocompact. We find out conditions under which an arbitrary product of spaces of the form locally- or almost locally-, becomes a space of the same form. We further show that is a free ideal (essential ideal) of C(X) if and only if is a free ideal (essential ideal) of when and only when X is locally- (almost locally-). We address the problem, when does or become identical to the socle of the ring C(X). The results obtained turn out to imply a special version of the fact obtained by Azarpanah corresponding to the choice ≡ the ideal of compact sets in X. Finally we observe that the ideals of the form of C(X) are no other than the z?-ideals of C(X). 相似文献
2.
《Quaestiones Mathematicae》2013,36(7):917-936
AbstractFor a free presentation 0 → τ → → → 0 of a Leibniz algebra , the Baer invariant is called the Schur multiplier of relative to the Liezation functor or Schur Lie-multiplier. For a two-sided ideal of a Leibniz algebra , we construct a four-term exact sequence relating the Schur Lie-multipliers of and /, which is applied to study and characterize Lie-nilpotency, Lie-stem covers and Lie-capability of Leibniz algebras. 相似文献
3.
The paper considers the equationwhere the operator-valued bounded functions aj and bj are 2π-periodic, and the operator-valued kernels m and n are 2π-periodic with respect to the first argument. The connection between the input-output stability of the equation and the invertibility of a family of operators acting on the space of periodic functions is investigated. 相似文献
4.
《Quaestiones Mathematicae》2013,36(7):857-884
AbstractLet be a standard operator algebra on an infinite dimensional complex Hilbert space containing identity operator I. In this paper it is shown that if is closed under the adjoint operation, then every multiplicative ?-Lie triple derivation is a linear ?-derivation. Moreover, if there exists an operator S ∈ such that S + S? = 0 then d(U) = U S ? SU for all U ∈ , that is, d is inner. Furthermore, it is also shown that any multiplicative ?-Lie triple higher derivation D = {δn}n∈? of is automatically a linear inner higher derivation on with d(U)? = d(U?). 相似文献
5.
《Quaestiones Mathematicae》2013,36(8):1045-1059
AbstractThe algebraic notion of a “congruence” seems to be foreign to contemporary graph theory. We propound that it need not be so by developing a theory of congruences of graphs: a congruence on a graph G = (V, E) being a pair (~, ) of which ~ is an equivalence relation on V and is a set of unordered pairs of vertices of G with a special relationship to ~ and E. Kernels and quotient structures are used in this theory to develop homomorphism and isomorphism theorems which remind one of similar results in an algebraic context. We show that this theory can be applied to deliver structural decompositions of graphs into “factor” graphs having very special properties, such as the result that each graph, except one, is a subdirect product of graphs with universal vertices. In a final section, we discuss corresponding concepts and briefly describe a corresponding theory for graphs which have a loop at every vertex and which we call loopy graphs. They are in a sense more “algebraic” than simple graphs, with their meet-semilattices of all congruences becoming complete algebraic lattices. 相似文献
6.
Jiren Zhou 《Quaestiones Mathematicae》2016,39(6):845-862
Let be a unital Banach algebra and be a unital -bimodule. A bilinear mapping α : is called a Hochschild 2-cocycle if xα(y, z) ? α(xy, z) + α(x, yz) ? α(x, y)z = 0 for any . We show that if δ is a linear mapping from into satisfying δ(xy) = δ(x)y + xδ(y) + α(x, y) for any with xy = W, where is a left or right separating point of , then δ is a generalized Jordan derivation associated with a Hochschild 2-cocycle α. We also find the relation of higher derivations and generalized derivations associated with Hochschild 2-cocycles. 相似文献
7.
《Quaestiones Mathematicae》2013,36(8):1091-1099
AbstractGiven a space X, we will say that a class of subsets of X is dominated by a class ? if for any A ∈ , there exists a B ∈ ? such that A ? . In particular, all (closed) discrete subsets of X are countably dominated (which we frequently abbreviate as ω-dominated) if, for any (closed) discrete set D ? X, there exists a countable set B ? X such that D ? . In this paper, we investigate the topological properties of spaces in which (closed) discrete subspaces are dominated either by countable subsets or by Lindelöf subspaces. 相似文献
8.
《Quaestiones Mathematicae》2013,36(8):985-995
AbstractIn this paper we give some equivalent conditions for the C. Huneke’s two conjectures concerning the finiteness properties of the local cohomology module , where R is a regular local ring, I is an ideal of R and i ≥ 0 is an integer. 相似文献
9.
Mehdi Parsinia 《Quaestiones Mathematicae》2018,41(5):675-682
Let X be a Tychono? space and A(X) be a subring of C(X) containing C?(X). We introduce the notion of -ideal in A(X). It is observed that the class of -ideals contains the class of zA-ideals and is contained in the class of z-ideals of A(X). These containments may be proper. It turns out that coincidence of z-ideals of A(X) with -ideals characterizes intermediate C-rings of C(X). 相似文献
10.
Michael Gil’ 《Quaestiones Mathematicae》2016,39(2):145-152
Let SNr (r ≥ 1) denote the Schatten-von Neumann ideal of compact operators in a separable Hilbert space. For the block matrixthe inequality(p = 2; 3;?…?) is proved, where λk(A) (k = 1; 2;?…?) are the eigenvalues of A and Nr(.) is the norm in SNr. Moreover, let P(z) = z2I + Bz + C (z ∈ ?) with B ∈ SN2p, C ∈ SNp. By zk(P) (k = 1; 2;?…?) the characteristic values of the pencil P are denoted. It is shown thatIn the case p = 1, sharper results are established. In addition, it is derived that 相似文献
11.
《Quaestiones Mathematicae》2013,36(6):765-779
AbstractAssume that is an ideal on ?, and ∑n xn is a divergent series in a Banach space X. We study the Baire category, and the measure of the set A() := {t ∈ {0, 1}?: ∑n t(n)xn is -convergent}. In the category case, we assume that has the Baire property and ∑n xn is not unconditionally convergent, and we deduce that A() is meager. We also study the smallness of A() in the measure case when the Haar probability measure λ on {0, 1}? is considered. If is analytic or coanalytic, and ∑n xn is -divergent, then λ(A()) = 0 which extends the theorem of Dindo?, ?alát and Toma. Generalizing one of their examples, we show that, for every ideal on ?, with the property of long intervals, there is a divergent series of reals such that λ(A(Fin)) = 0 and λ(A()) = 1. 相似文献
12.
《Quaestiones Mathematicae》2013,36(4):551-560
AbstractIn the paper extended Keller graph is defined and some of its properties, such as Hamiltonian, the independence number, the chromatic number, etc., are proved. Moreover, the size of a maximum clique of for d = 2, 3, 4 and d ≥ 8 is given and for d = 5, 6, 7 a conjecture is stated. 相似文献
13.
Vladimir V. Tkachuk 《Quaestiones Mathematicae》2018,41(6):729-743
We present a study of two versions of the point-picking game defined by Berner and Juhasz. Given a space X there are two rivals O and P who take turns playing on X. In the n-th round Player O takes a non-empty open subset Un of the space X and P responds by choosing a point xn ∈ Un. After ω-many moves are completed, the family is called the play of the game. In the CD-game CD(X) Player P wins if the set is closed and discrete. Otherwise O is the winner. In the CL-game CL(X, p), where the point p ∈ X is fixed, Player O wins if contains p in its closure. If , then P is declared to be the winner. We show that in spaces Cp(X) both CD-game and CL-game are equivalent to Gruenhage’s W-game for Player O. If , then Player O has a winning strategy in CL(X, p). The converse is not always true. However, if X is separable or compact of π-weight ≤ ω1, then existence of a winning strategy for O in CL(X, p) is equivalent to . 相似文献
14.
In every finite poset (X, ≤) we assign the so called order-matrix , where αij ∈ {?2, 0, 1, 2}. Using this matrix, we characterize the order dimension of an arbitrary finite poset. 相似文献
15.
Marian Nowak 《Quaestiones Mathematicae》2019,42(1):113-124
Let B() denote the Banach algebra of all bounded Borel measurable complex functions defined on a topological Hausdor? space X, and Bo() stand for the ideal of B() consisting of all functions vanishing at infinity. Then B() is a faithful Banach left Bo()-module and the strict topology β on B() induced by Bo() is a mixed topology. For a sequentially complete locally convex Hausdor? space (E, ξ), we study the relationship between vector measures m : → E and the corresponding continuous integration operators Tm : B() → E. It is shown that a measure m : → E is countably additive tight if and only if the corresponding integration operator Tm is (η, ξ)-continuous, where η denotes the infimum of the strict topology β and the Mackey topology τ (B(), ca()). If, in particular, E is a Banach space, it is shown that m is countably additive tight if and only if Tm(absconv(U ∪ W)) is relatively weakly compact in E for some τ (B(), ca())-neighborhood U of 0 and some β-neighborhood W of 0 in B(). As an application, we prove a Nikodym type convergence theorem for countably additive tight vector measures. 相似文献
16.
In this paper we prove that the Fremlin tensor product of two f-algebras can be endowed with an f-algebra structure and satisfies an appropriate universal property. In particular, the Riesz tensor product of C(X) and C(Y), where X and Y are topological spaces, is an f-subalgebra of C(X × Y). 相似文献
17.
We consider the discrete right definite Sturm-Liouville problems with nonlinear eigenparameter dependent boundary conditions,where T > 1 is an integer and λ is the spectrum parameter. We obtain the existence of the eigenvalues, the oscillation properties of the eigenfunctions and the interlacing results of the eigenvalues of the above problem with the eigenvalues of the Dirichlet problem and the Neumann problem. 相似文献
18.
We explore some parallelism between the categories CRFrm and 0DFrm of completely regular frames and zero-dimensional frames, respectively, with a view to establishing zero-dimensional analogues of C*-quotients. A lattice homomorphism between the cozero parts of two completely regular frames can be lifted to a frame homomorphism between the Stone-?ech compactifications of the frames involved [13]. Here we lift a lattice homomorphism ψ: BL → BM between the Boolean parts of two zero-dimensional frames to a frame homomorphism between their universal zero-dimensional compactifications, and then study some properties of the lift. 相似文献
19.
《Quaestiones Mathematicae》2013,36(5):665-672
AbstractIn this note, we introduce (hereditary) Amitsur rings and give examples of (hereditary) Amitsur rings. We construct radicals and S. We also find radicals in which every prime ring is a hereditary Amitsur ring and radicals in which every prime ring is not a hereditary Amitsur ring. We give characterizations for (hereditary) Amitsur rings and prove that the semisimple class SS is polynomial extensible. We show that all zero rings are Amitsur rings and all Baer radical rings are hereditary Amitsur rings. 相似文献