共查询到20条相似文献,搜索用时 31 毫秒
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The aim of this paper is to give a characterization of path connected topological fields, inspired by the classical Gelfand correspondence between a compact Hausdorff topological space X and the space of maximal ideals of the ring of real valued continuous functions . More explicitly, our motivation is the following question: What is the essential property of the topological field that makes such a correspondence valid for all compact Hausdorff spaces? It turns out that such a perfect correspondence exists if and only if F is a path connected topological field. 相似文献
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Imanol Mozo Carollo 《Journal of Pure and Applied Algebra》2021,225(2):106490
This paper approaches the construction of the universal completion of the Riesz space of continuous real functions on a completely regular frame L in two different ways. Firstly as the space of continuous real functions on the Booleanization of L. Secondly as the space of nearly finite Hausdorff continuous functions on L. The former has no counterpart in the classical theory, as the Booleanization of a spatial frame is not spatial in general, and it offers a lucid way of representing the universal completion as a space of continuous real functions. As a corollary we obtain that and have isomorphic universal completions if and only if the Booleanization of L and M are isomorphic and we characterize frames L such that is universally complete as almost Boolean frames. The application of this last result to the classical case of the space of continuous real functions on a topological space X characterizes those spaces X for which is universally complete. Finally, we present a pointfree version of the Maeda-Ogasawara-Vulikh representation theorem and use it to represent the universal completion of an Archimedean Riesz space with weak unit as a space of continuous real functions on a Boolean frame. 相似文献
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Judit Abardia-Evéquoz Károly J. Böröczky Mátyás Domokos Dávid Kertész 《Journal of Functional Analysis》2019,276(11):3325-3362
The space of continuous, -equivariant, , and translation covariant valuations taking values in the space of real symmetric tensors on of rank is completely described. The classification involves the moment tensor valuation for and is analogous to the known classification of the corresponding tensor valuations that are -equivariant, although the method of proof cannot be adapted. 相似文献
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As an extension of Gabor frames, nonstationary Gabor (NSG) frames were recently introduced in adaptive signal analysis. They allow for efficient reconstruction with flexible sampling and varying window functions. In this paper we generalize the notion of NSG frames from to the vector-valued Hilbert space , and investigate the resulting vector-valued NSG frames. We derive a Walnut's representation of the mixed frame operator, and provide some necessary/sufficient conditions for a vector-valued NSG system to be a frame for . Furthermore, we show the existence of painless vector-valued NSG frames, and of vector-valued NSG frames with fast decaying window functions. 相似文献
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Javier Jiménez-Garrido Javier Sanz Gerhard Schindl 《Journal of Mathematical Analysis and Applications》2019,469(1):136-168
We consider Roumieu–Carleman ultraholomorphic classes and classes of functions admitting asymptotic expansion in unbounded sectors, defined in terms of a log-convex sequence . Departing from previous results by S. Mandelbrojt and B. Rodríguez-Salinas, we completely characterize the injectivity of the Borel map by means of the theory of proximate orders: A growth index turns out to put apart the values of the opening of the sector for which injectivity holds or not. In the case of surjectivity, we considerably extend partial results by J. Schmets and M. Valdivia and by V. Thilliez, and prove a similar dividing character for the index (introduced by Thilliez, and generally different from ) in some standard situations (for example, as far as is strongly regular). 相似文献
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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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Let be a rational expression of degree three over the finite field . We count the irreducible polynomials in , of a given degree, that have the form for some . As an example of application of our results, we recover the number of irreducible transformation shift registers of order three, which were computed by Jiang and Yang in 2017. 相似文献
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We provide a generalization of pseudo-Frobenius numbers of numerical semigroups to the context of the simplicial affine semigroups. In this way, we characterize the Cohen-Macaulay type of the simplicial affine semigroup ring . We define the type of S, , in terms of some Apéry sets of S and show that it coincides with the Cohen-Macaulay type of the semigroup ring, when is Cohen-Macaulay. If is a d-dimensional Cohen-Macaulay ring of embedding dimension at most , then . Otherwise, might be arbitrary large and it has no upper bound in terms of the embedding dimension. Finally, we present a generating set for the conductor of S as an ideal of its normalization. 相似文献
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