共查询到7条相似文献，搜索用时 0 毫秒
1.
Ignacio Villanueva 《Proceedings of the American Mathematical Society》2000,128(3):793-801
Given a -linear operator from a product of spaces into a Banach space , our main result proves the equivalence between being completely continuous, having an -valued separately continuous extension to the product of the biduals and having a regular associated polymeasure. It is well known that, in the linear case, these are also equivalent to being weakly compact, and that, for , being weakly compact implies the conditions above but the converse fails.
2.
The paper is concerned with order-topological characterizations of topological Riesz spaces, in particular spaces of measurable functions, not containing Riesz isomorphic or linearly homeomorphic copies of or .
3.
Mikhail G. Tkacenko Vladimir V. Tkachuk Richard G. Wilson Ivan V. Yaschenko 《Proceedings of the American Mathematical Society》2000,128(1):287-297
Two -topologies and given on the same set , are called transversal if their union generates the discrete topology on . The topologies and are -complementary if they are transversal and their intersection is the cofinite topology on . We establish that for any connected Tychonoff topology there exists a connected Tychonoff transversal one. Another result is that no -complementary topology exists for the maximal topology constructed by van Douwen on the rational numbers. This gives a negative answer to Problem 162 from Open Problems in Topology (1990).
4.
Elijah Liflyand Ferenc Mó ricz 《Proceedings of the American Mathematical Society》2000,128(5):1391-1396
We prove that the Hausdorff operator generated by a function is bounded on the real Hardy space . The proof is based on the closed graph theorem and on the fact that if a function in is such that its Fourier transform equals for (or for ), then .
5.
Daniel Wulbert 《Proceedings of the American Mathematical Society》2000,128(8):2431-2438
Let be a -finite, nonatomic, Baire measure space. Let be a finite dimensional subspace of . There is a bounded, continuous function, , defined on , such that
(1) for all , and (2) almost everywhere.
6.
The main result of this paper is that every nonreflexive subspace of fails the fixed point property for closed, bounded, convex subsets of and nonexpansive (or contractive) mappings on . Combined with a theorem of Maurey we get that for subspaces of , is reflexive if and only if has the fixed point property. For general Banach spaces the question as to whether reflexivity implies the fixed point property and the converse question are both still open.
7.
The paper deals with the impulsive nonlinear boundary value problem