共查询到20条相似文献,搜索用时 15 毫秒
1.
N. M. Pyrch 《Journal of Mathematical Sciences》2010,168(4):585-589
We have established the topological properties of free homogeneous spaces and studied the action of the functor of a free
homogeneous space on pairs of topological spaces. 相似文献
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The theory of metrically generated constructs provides us with an excellent setting for the study of function spaces. In this paper we develop a function space theory for metrically generated constructs and, by considering different metrically generated constructs, we capture interesting examples. For instance, for uniform spaces we retrieve the uniformity of uniform convergence and its generalization to Σ-convergence and for UG-spaces we obtain a quantified version of these structures. Our theory also allows for many applications, in particular we are able to characterize the complete subspaces of these function spaces and we succeed in producing an appropriate Ascoli theorem. 相似文献
4.
V. I. Malykhin 《Mathematical Notes》1998,64(5):607-615
The presence of disjoint dense (Borel) subsets in Tychonoff cubes, Borel subspaces of Tychonoff cubes, and dyadic compacta
is examined. Several problems are stated.
Translated fromMatematicheskie Zametki, Vol. 64, No. 5, pp. 701–712, November, 1998.
The author wishes to express his gratitude to V. Shchigolev for fruitful discussion of some questions touched upon in this
paper and to the referee for valuable comments and suggestions concerning the style and the content.
This research was supported by the Russian Foundation for Basic Research under grant No. 96-01-01619. 相似文献
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Aicke Hinrichs 《Proceedings of the American Mathematical Society》2006,134(3):731-735
A well-known multiplicative Weyl inequality states that the sequence of eigenvalues and the sequence of approximation numbers of any compact operator in a Banach space satisfy
for all . We prove here that the constant is optimal, which solves a longstanding problem.
for all . We prove here that the constant is optimal, which solves a longstanding problem.
9.
We discuss algebraic properties of the Weyl product acting on modulation spaces. For a certain class of weight functions ω we prove that is an algebra under the Weyl product if p∈[1,∞] and 1?q?min(p,p′). For the remaining cases p∈[1,∞] and min(p,p′)<q?∞ we show that the unweighted spaces Mp,q are not algebras under the Weyl product. 相似文献
10.
Paolo Boggiatto Giuseppe De Donno Alessandro Oliaro 《Mathematische Nachrichten》2009,282(12):1656-1663
We study boundedness and compactness properties for the Weyl quantization with symbols in Lq (?2d ) acting on Lp (?d ). This is shown to be equivalent, in suitable Banach space setting, to that of the Wigner transform. We give a short proof by interpolation of Lieb's sufficient conditions for the boundedness of the Wigner transform, proving furthermore that these conditions are also necessary. This yields a complete characterization of boundedness for Weyl operators in Lp setting; compactness follows by approximation. We extend these results defining two scales of spaces, namely L*q (?2d ) and L?q (R2d ), respectively smaller and larger than the Lq (?2d ),and showing that the Weyl correspondence is bounded on L*q (R2d ) (and yields compact operators), whereas it is not on L?q (R2d ). We conclude with a remark on weak‐type Lp boundedness (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
11.
Dense linear subspaces of quasinormable Fréchet spaces need not be quasinormable, as an example due to J. Bonet and S. Dierolf proved. A characterization of the quasinormability of dense linear subspaces of quasinormable locally convex spaces and several consequences are given. Moreover, an example of a dense linear subspace of a countable direct sum of Banach spaces, which is not quasinormable, is provided. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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The underlying metric affine geometry, or metric projective geometry, can be recovered from Grassmann spaces associated with the family of regular subspaces of respective space. In other words, automorphisms of such Grassmann spaces are collineations witch preserve orthogonality of the respective underlying space. This generalizes results of Pra?mowska et al. (Linear Algebra Appl 430:3066–3079, 2009) and Pra?mowska and ?ynel (Adv Geom, to appear). 相似文献
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M. M. Dragilev 《Siberian Mathematical Journal》1996,37(3):490-499
14.
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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On subspaces of pseudoradial spaces 总被引:1,自引:0,他引:1
A topological space is pseudoradial if each of its non closed subsets has a sequence (not necessarily with countable length) convergent to outside of . We prove the following results concerning pseudoradial spaces and the spaces , where is an ultrafilter on :
(i) CH implies that, for every ultrafilter on , is a subspace of some regular pseudoradial space.
(ii) There is a model in which, for each P-point , cannot be embedded in a regular pseudoradial space while there is a point such that is a subspace of a zero-dimensional Hausdorff pseudoradial space.
17.
In the paper we construct a system of bounded functions which generates an uncomplemented subspace in the Lorentz space Λ(α) for all α∈(0,1). Lower bounds of the norms of the projector onto such subspaces are obtained. Translated fromMatematicheskie Zametki, Vol. 68, No. 1, pp. 57–65, July, 2000. 相似文献
18.
Some criterions in order thatl
1 embeds complementably inE
Φ(μ) and inL
Φ(μ) are given. It is also proved that every idealL inL
Φ(μ) such thatI
Φ(x/‖x‖Φ)=1 for anyxεL/{0} is contained inE
Φ(μ). 相似文献
19.
In this paper we study the problems of existence of noncomplemented subspaces and Lozinsky-Kharshilade systems [10] in Banach
spaces not isomorphic to Hilbert spaces.
Supported by N.S.F. Grant number GP-6152
Supported by N.S.F. Grant number GP-2242 相似文献
20.
M.S. Asgari 《Journal of Mathematical Analysis and Applications》2005,308(2):541-553
In this paper we develop the frame theory of subspaces for separable Hilbert spaces. We will show that for every Parseval frame of subspaces {Wi}i∈I for a Hilbert space H, there exists a Hilbert space K⊇H and an orthonormal basis of subspaces {Ni}i∈I for K such that Wi=P(Ni), where P is the orthogonal projection of K onto H. We introduce a new definition of atomic resolution of the identity in Hilbert spaces. In particular, we define an atomic resolution operator for an atomic resolution of the identity, which even yield a reconstruction formula. 相似文献