共查询到20条相似文献,搜索用时 15 毫秒
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This paper contains a unified simple approach to the main theorems on ordinary differential equations in ordered Banach spaces when the positive cone has a nonempty interior. The main features are (i) the inclusion of the case of absolutely continuous functions where the differential inequality holds only a.e.; (ii) the different situation corresponding to weak or strong inequalities in the initial conditions. An application to matrix differential equations yields generalizations of known theorems for matrix Riccati equations, among others.Dedicated to professor E. Hlawka on the occasion of his seventieth birthdayGuest professor at the Mathematisches Institut I, University of Karlsruhe, under auspices of the U.S. Special Program, Alexander von Humboldt-Stiftung. 相似文献
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Tepper L. Gill Sudeshna Basu Woodford W. Zachary V. Steadman 《Proceedings of the American Mathematical Society》2004,132(5):1429-1434
In this paper we show that a result of Gross and Kuelbs, used to study Gaussian measures on Banach spaces, makes it possible to construct an adjoint for operators on separable Banach spaces. This result is used to extend well-known theorems of von Neumann and Lax. We also partially solve an open problem on the existence of a Markushevich basis with unit norm and prove that all closed densely defined linear operators on a separable Banach space can be approximated by bounded operators. This last result extends a theorem of Kaufman for Hilbert spaces and allows us to define a new metric for closed densely defined linear operators on Banach spaces. As an application, we obtain a generalization of the Yosida approximator for semigroups of operators.
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Valentin Ferenczi 《Journal of Functional Analysis》2009,257(1):149-1060
We prove three new dichotomies for Banach spaces à la W.T. Gowers' dichotomies. The three dichotomies characterise respectively the spaces having no minimal subspaces, having no subsequentially minimal basic sequences, and having no subspaces crudely finitely representable in all of their subspaces. We subsequently use these results to make progress on Gowers' program of classifying Banach spaces by finding characteristic spaces present in every space. Also, the results are used to embed any partial order of size ℵ1 into the subspaces of any space without a minimal subspace ordered by isomorphic embeddability. 相似文献
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有序Banach空间常微分方程的正周期解 总被引:1,自引:0,他引:1
依据凝聚锥映射的一个krasnoselskii型不动点定理,在有序Banach空间中获得了二阶常微分方程.-u^n(t) Mu(t)=f(t,u(t))正ω—周期解的存在性结果。 相似文献
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Pradipta Bandyopadhyay S. Dutta 《Proceedings of the American Mathematical Society》2004,132(1):107-115
In this paper, we obtain some sufficient conditions for an almost constrained subspace to be constrained (in fact, by a unique norm 1 projection), which improves significantly upon all existing conditions of similar type with significantly simpler proofs.
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Ivan Singer 《Journal of Functional Analysis》1973,13(3):223-232
As natural generalizations of complemented subspaces, we introduce pseudo-complemented and strongly pseudo-complemented subspaces of Banach spaces, and we study for such subspaces some of the problems analogous to the classical problems on complemented and quasi-complemented subspaces. 相似文献
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关于Banach空间隐式常微分方程的解的存在性 总被引:3,自引:0,他引:3
林艺 《纯粹数学与应用数学》1999,15(3):68-72
讨论了 Banach 空间中隐式常微分方程 F(t,x,x′) = 0, x(t0 ) = x0 , x′(t0) = y0 的解的存在性,其中, F 的定义域可含无穷远点 相似文献
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Joram Lindenstrauss 《Israel Journal of Mathematics》1968,6(1):36-38
It is proved that for uncountableΓ,c
0(Γ) has no quasicomplement inm(Γ).
Research supported by the National Science Foundation, U.S.A. 相似文献
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J. Harjani K. Sadarangani 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(3-4):1188-1197
The purpose of this paper is to present some fixed point theorems in a complete metric space endowed with a partial order by using altering distance functions. We also present some applications to first and second order ordinary differential equations. 相似文献
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The common Banach spaces are investigated with respect to some properties of their finite dimensional subspaces.
The contribution to the paper of the second author is part of his Ph.D. thesis prepared at the Hebrew University of Jerusalem
under the supervision of Professor A. Dvoretzky. The authors wish to thank Professor A. Dvoretzky for the interest he showed
in the paper and for his helpful advice. 相似文献
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In this paper we obtain new estimates for the relative projection constants of subspaces of a Banach spaceY in terms of geometrical properties ofY. Our method gives thatK-convex spaces are locally π-Euclidean. We also get a version of Maurey’s extension theorem for spaces of typep<2. 相似文献
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Alex Chigogidze 《Proceedings of the American Mathematical Society》2001,129(10):2959-2963
We show that complemented subspaces of uncountable products of Banach spaces are products of complemented subspaces of countable subproducts.
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