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1.
《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
2.
Assume that X, Y are real Banach spaces, Y has uniform convexity of type p (≥ 1), and f: X → Y is a standard coarse isometry. In this paper, we show that if
then there is a linear isometry U : X → Y so that
where is defined by
Representation properties of coarse isometries in free ultrafilter limits on are also discussed. 相似文献
3.
《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
4.
《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
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《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
6.
《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
7.
《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
8.
《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
9.
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
10.
《Quaestiones Mathematicae》2013,36(7):977-983
AbstractA practical number is a positive integer n such that all the positive integers m ≤ n can be written as a sum of distinct divisors of n. Let (un)n≥0 be the Lucas sequence satisfying u0 = 0, u1 = 1, and un+2 = aun+1 + bun for all integers n ≥ 0, where a and b are fixed nonzero integers. Assume a(b + 1) even and a2 + 4b > 0. Also, let be the set of all positive integers n such that |un| is a practical number. Melfi proved that is infinite. We improve this result by showing that #(x) ? x/log x for all x ≥ 2, where the implied constant depends on a and b. We also pose some open questions regarding . 相似文献
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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
13.
《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
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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
16.
《Quaestiones Mathematicae》2013,36(3):401-414
AbstractA connected graph G is a cactus if any two of its cycles have at most one common vertex. Denote by the set of n-vertex cacti with matching number q. Huang, Deng and Simi? [23] identified the unique graph with the maximum spectral radius among 2q-vertex cacti with perfect matchings. In this paper, as a continuance of it, the largest and second largest spectral radii together with the corresponding graphs among are determined. Consequently, the first two largest spectral radii together with cacti having perfect matchings are also determined. 相似文献
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《Quaestiones Mathematicae》2013,36(6):803-809
AbstractIn this paper, we have extended a known theorem dealing with |, pn|k summability factors to the |A, pn|k summability under weaker conditions by using an almost increasing sequence 相似文献
19.
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
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