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1.
In this paper, we study lattices of preradicals which are not small classes (in which case we say that the corresponding rings are p-large), and specially we consider some infinite representation type algebras. We construct an injective assignment between lattices of preradicals, using a full functor between the corresponding categories of modules, that satisfies certain conditions. We show that the polynomial ring over any field is p-large, and we use this fact to provide examples and some classes of algebras (both tame and wild) which are p-large. 相似文献
2.
We give several applications of Rademacher sequences in abstract Banach lattices. We characterise those Banach lattices with an atomic dual in terms of weak* sequential convergence. We give an alternative treatment of results of Rosenthal, generalising a classical result of Pitt, on the compactness of operators from Lp into Lq. Finally we generalise earlier work of ours by showing that, amongst Banach lattices F with an order continuous norm, those having the property that the linear span of the positive compact operators fromE into F is complete under the regular norm for all Banach lattices E are precisely the atomic lattices. 相似文献
3.
Benyamini Yoav; Lassalle Silvia; Llavona Jose G. 《Bulletin London Mathematical Society》2006,38(3):459-469
The main result in this paper is a representation theorem forhomogeneous orthogonally additive polynomials on Banach lattices.The representation theorem is used to study the linear spanof the set of zeros of homogeneous real-valued orthogonallyadditive polynomials. It is shown that in certain lattices everyelement can be represented as the sum of two or three zerosor, at least, can be approximated by such sums. It is also indicatedhow these results can be used to study weak topologies inducedby orthogonally additive polynomials on Banach lattices. 2000Mathematics Subject Classification 46G25, 46B42, 47B38. 相似文献
4.
S. Argyros 《Israel Journal of Mathematics》1980,37(1-2):21-33
The isomorphic embedding of the Banach spacel
i(Γ) into injective Banach spaces is investigated. 相似文献
5.
We study the restriction to smaller subgroups, of cohomology classes on arithmetic groups (possibly after moving the class
by Hecke correspondences), especially in the context of first cohomology of arithmetic groups. We obtain vanishing results for the first cohomology of cocompact arithmetic lattices in SU(n,1) which arise from hermitian forms over division algebras D of degree p
2, p an odd prime, equipped with an involution of the second kind. We show that it is not possible for a ‘naive’ restriction of
cohomology to be injective in general. We also establish that the restriction map is injective at the level of first cohomology
for non co-compact lattices, extending a result of Raghunathan and Venkataramana for co-compact lattices.
Received: 14 September 2000 / Accepted: 6 June 2001 相似文献
6.
We find large classes of injective and projective p-multinormed spaces. In fact, these classes are universal, in the sense that every p-multinormed space embeds into (is a quotient of) an injective (resp. projective) p-multinormed space. As a consequence, we show that any p-multinormed space has a canonical representation as a subspace of a quotient of a Banach lattice. 相似文献
7.
We introduce UDS
p
-property (resp. UDT
q
-property) in Banach lattices as the property that every normalized disjoint sequence has a subsequence with an upper p-estimate (resp. lower q-estimate). In the case of rearrangement invariant spaces, the relationships with Boyd indices of the space are studied. Some
applications of these properties are given to the high order smoothness of Banach lattices, in the sense of the existence
of differentiable bump functions 相似文献
8.
9.
Guillermo P. Curbera 《Indagationes Mathematicae》2006,17(2):187-204
New features of the Banach function space L1w(v), that is, the space of all v-scalarly integrable functions (with v any vector measure), are exposed. The Fatou property plays an essential role and leads to a new representation theorem for a large class of abstract Banach lattices. Applications are also given to the optimal domain of kernel operators taking their values in a Banach function space. 相似文献
10.
Bojan Kuzma 《Czechoslovak Mathematical Journal》2006,56(3):919-921
It is proved that a linear surjection Ф: A → B, which preserves noninvertibility between semisimple, unital, complex Banach algebras, is automatically injective. 相似文献
11.
In this paper, we first introduce a lattice decomposition and finite-dimensional lattice decomposition (FDLD) for Banach lattices. Then we show that for a Banach lattice with FDLD, the following are equivalent: (i) it has the Radon-Nikodym property; (ii) it is a KB-space; (iii) it is a Levi space; and (iv) it is a σ-Levi space. We then give a sequential representation of the Fremlin projective tensor product of an atomic Banach lattice with a Banach lattice. Using this sequential representation, we show that if one of the Banach lattices X and Y is atomic, then the Fremlin projective tensor product has the Radon-Nikodym property (or, respectively, is a KB-space) if and only if both X and Y have the Radon-Nikodym property (or, respectively, are KB-spaces). 相似文献
12.
Measures of Non-compactness of Operators on Banach Lattices 总被引:1,自引:0,他引:1
[Indag. Math.(N.S.)
2(2) (1991), 149–158; Uspehi Mat. Nauk
27(1(163)) (1972), 81–146] used representation spaces to study measures of non-compactness and spectral radii of operators on Banach lattices. In this paper, we develop representation spaces based on the nonstandard hull construction (which is equivalent to the ultrapower construction). As a particular application, we present a simple proof and some extensions of the main result of [J. Funct. Anal. 78(1) (1988), 31–55] on the monotonicity of the measure of non-compactness and the spectral radius of AM-compact operators. We also use the representation spaces to characterize d-convergence and discuss the relationship between d-convergence and the measures of non-compactness. 相似文献
13.
In analogy to the situation for continuous lattices which were introduced by Dana Scott as precisely the injective T0 spaces via the (nowadays called) Scott topology, we study those metric spaces which correspond to injective T0 approach spaces and characterise them as precisely the continuous lattices equipped with a unitary and associative [0,?∞?]-action. This result is achieved by a detailed analysis of the notion of cocompleteness for approach spaces. 相似文献
14.
15.
We consider n-dimensional real Banach spaces X which are far, in the Banach–Mazur distance, from all complemented subspaces of all Banach lattices. We show that this is related to the volume ratio values of X with respect to ellipsoids and to zonoids. 相似文献
16.
We study summing multipliers from Banach spaces of analytic functions on the unit disc of the complex plane to the complex Banach sequence lattices. The domain spaces are abstract variants of the classical Hardy spaces generated by the complex symmetric spaces. Applying interpolation methods, we prove the Hausdorff Young and Hardy-Littlewood type theorems. We show applications of these results to study summing multipliers from the Hardy-Orlicz spaces to the Orlicz sequence lattices. The obtained results extend the well-known results for the Hp spaces. 相似文献
17.
Chen Zili 《数学学报(英文版)》1988,4(4):301-308
The Grothendieck's criterion of weak compactness in spaceC(S) has been extended by C.P.Niculescu for weakly sequentially complete Banach lattices. This paper first provides some sufficient
and necessary conditions for weakly sequentially complete Banach lattices, with the result that the criterion C.P.Niculescu
obtained of the weak compactness has actually characterized the weakly sequentially Banach lattices. At the same time we extend
C.P.Niculescu's important results.
Then we solve negatively Problem 1.11 which was posed by C.P.Niculescu, and a sufficient condition for this is given which
generalizes Pelczyński's result. 相似文献
18.
Helmut H. Schaefer 《Israel Journal of Mathematics》1972,13(3-4):400-415
On the tensor productE⊗F of a pair of order complete Banach lattices, two cross norms (called thel-andm-norm, respectively) are introduced. These cross-norms (which depend on the order of factors, and are permuted when the latter
is inverted) have the property that the respective completions ofE⊗F are Banach lattices under the ordering defined by the closure of the projective cone. Moreover, they are self-dual with respect
to <E ⊗F, E’> and coincide with well-known tensor norms in important special cases. 相似文献
19.
Ondej F.K. Kalenda 《Journal of Mathematical Analysis and Applications》2009,350(2):464-484
We collect examples of Valdivia compact spaces, their continuous images and associated classes of Banach spaces which appear naturally in various branches of mathematics. We focus on topological constructions generating Valdivia compact spaces, linearly ordered compact spaces, compact groups, L1 spaces, Banach lattices and noncommutative L1 spaces. 相似文献
20.
《Indagationes Mathematicae (Proceedings)》1989,92(1):35-47
In this paper we give a characterization of dual Banach lattices. In fact, we prove that a Banach function space E on a separable measure space which has the Fatou property is a dual Banach lattice if and only if all positive operators from L1(0,1) into E are abstract kernel operators, hence extending the fact, proved by M. Talagrand, that separable Banach lattices with the Radon-Nikodym property are dual Banach lattices. 相似文献