共查询到20条相似文献,搜索用时 13 毫秒
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E. V. Tokarev 《Functional Analysis and Its Applications》1981,15(2):150-151
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Minimal and reflexive Banach lattices 总被引:1,自引:0,他引:1
Heinrich P. Lotz 《Mathematische Annalen》1974,209(2):117-126
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Reflexivity in Banach lattices 总被引:1,自引:0,他引:1
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《Journal of Functional Analysis》2023,284(10):109888
The construction of the free Banach lattice generated by a real Banach space is extended to the complex setting. It is shown that for every complex Banach space E there is a complex Banach lattice containing a linear isometric copy of E and satisfying the following universal property: for every complex Banach lattice , every operator admits a unique lattice homomorphic extension with . The free complex Banach lattice is shown to have analogous properties to those of its real counterpart. However, examples of non-isomorphic complex Banach spaces E and F can be given so that and are lattice isometric. The spectral theory of induced lattice homomorphisms on is also explored. 相似文献
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Tadeusz Figiel William B. Johnson Aleksander Pe?czyński 《Israel Journal of Mathematics》2011,183(1):199-231
The notion of the bounded approximation property = BAP (resp. the uniform approximation property = UAP) of a pair [Banach space, its subspace] is used to prove that if X is a ℒ
∞-space, Y a subspace with the BAP (resp. UAP), then the quotient X/Y has the BAP (resp. UAP). If Q: X → Z is a surjection, X is a ℒ
1-space and Z is a ℒ
p
-space (1 ≤ p ≤ ∞), then ker Q has the UAP. A complemented subspace of a weakly sequentially complete Banach lattice has the separable complementation property = SCP.
A criterion for a space with GL-l.u.st. to have the SCP is given. Spaces which are quotients of weakly sequentially complete
lattices and are uncomplemented in their second duals are studied. Examples are given of spaces with the SCP which have subspaces
that fail the SCP. The results are applied to spaces of measures on a compact Abelian group orthogonal to a fixed Sidon set
and to Sobolev spaces of functions of bounded variation on ℝ
n
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Egbert Dettweiler 《Mathematische Zeitschrift》1982,181(3):411-434
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William Feldman 《Mathematische Zeitschrift》1988,199(4):549-553
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Michel Talagrand 《Israel Journal of Mathematics》1981,38(1-2):46-50
We construct a separable dual Banach latticeE such that no non-trivial order interval of its dual is weakly compact. HenceE has the Radon-Nikodym property without being in some sense a dual in a natural way.
The final draft of this paper was written while the author held a grant from NATO to visit the Ohio State University. 相似文献
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Disjoint sequence methods from the theory of Riesz spaces are used to study compact operators on Banach lattices. A principal
new result of the paper is that each positive map from a Banach latticeE to a Banach latticeF with compact majorant is itself compact provided the norms onE′ andF are order continuous. 相似文献
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G. Ya. Lozanovskii 《Mathematical Notes》1968,4(1):514-516
A generalization is given of the familiar result of Philips on the nonexistence of a projector from m onto c0. The results obtained imply, for example, the following consequence. Ifthe Orlicz space L
M
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EM, there is no projector from L
M
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onto EM and EM is not isomorphic to any conjugate Banach space.Translated from Matematicheskie Zametki, Vol. 4, No. 1, pp. 41–44, July, 1968. 相似文献
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Peter Ørno 《Israel Journal of Mathematics》1974,19(3):264-265
Let Λ1 and Λ2 be infinte-dimensional, Banach lattices such thatc o is not finitely representable in Λ2. Then the bounded linear operators from Λ1 to Λ2 form a lattice if and only if Λ1 is an abstract AL space. 相似文献
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