共查询到20条相似文献,搜索用时 10 毫秒
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Acta Mathematica Hungarica - We deal with isomorphic Banach–Stone type theorems for closed subspaces of vectorvalued continuous functions. Let $$\mathbb{F}=\mathbb{R}$$ or $$\mathbb{C}$$ .... 相似文献
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É. N. Morozov 《Mathematical Notes》1976,19(3):209-212
It is shown that if on a compact space Q any polynomial
0} $$
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, in a system of continuous vector functions with real coefficients such that N=n·s and s=2p +1 has at most n–1 zeros, then Q is homeomorphic to a circle or a part of one.Translated from Matematicheskie Zametki, Vol. 19, No. 3, pp. 347–352, March 1976.In conclusion, the author thanks S. B. Stechkin for stating the problem globally. 相似文献
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We study non-linear maps on the set of n × n matrices over a field, which preserve the zeros of a fixed homogeneous multilinear polynomial. This solves Kaplansky-Watkins
problem from 1976 about the structure of such transformations.
Published in Russian in Doklady Akademii Nauk, 2009, Vol. 427, No. 3, pp. 300–302.
Presented by Academician A.T. Fomenko December 8, 2008
The article was translated by the authors. 相似文献
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Jesú s Araujo Juan J. Font 《Transactions of the American Mathematical Society》1997,349(1):413-428
We say that a linear subspace of is strongly separating if given any pair of distinct points of the locally compact space , then there exists such that . In this paper we prove that a linear isometry of onto such a subspace of induces a homeomorphism between two certain singular subspaces of the Shilov boundaries of and , sending the Choquet boundary of onto the Choquet boundary of . We also provide an example which shows that the above result is no longer true if we do not assume to be strongly separating. Furthermore we obtain the following multiplicative representation of : for all and all , where is a unimodular scalar-valued continuous function on . These results contain and extend some others by Amir and Arbel, Holszty\'{n}ski, Myers and Novinger. Some applications to isometries involving commutative Banach algebras without unit are announced.
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Maps completely preserving spectral functions 总被引:1,自引:0,他引:1
Let X,Y be infinite dimensional complex Banach spaces and A,B be standard operator algebras on X and Y, respectively. In this paper, we show that surjective maps completely preserving certain spectral function Δ(·) from A to B are isomorphisms, where Δ(·) stands for any one of 13 spectral functions σ(·), σl(·), σr(·), σl(·)∩σr(·), ∂σ(·), ησ(·), σp(·), σc(·), σp(·)∩σc(·), σp(·)∪σc(·), σap(·), σs(·), and σap(·)∩σs(·). 相似文献
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Summary We study completeness of weighted spaces of vector-valued functions. Also, the dual of a weighted space of vector-valued continuous
functions on a locally compact space is characterized as a space of vector valued Radon measures with values in the topological
dual of the range space.
Research supported by a grant from the National Science Foundation, GP 22713.
Entrata in Redazione il 25 ottobre 1970. 相似文献
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Michael Cambern 《Journal of Mathematical Analysis and Applications》1977,57(2):290-297
In this article we obtain, for 1 ? p ? ∞, a characterization of the invariant subspaces of spaces of vector-valued Lp functions defined on the unit circle—i.e., of those subspaces invariant under multiplication by eix. This result is then applied to extend, to the corresponding Hardy classes of vector-valued functions, the known characterizations of the extreme points of the unit ball in the scalar Hardy classes H1 and H∞. Finally, it is shown that the characterization of the closure of the set of extreme points of the unit ball in H1 changes significantly when we pass from the scalar to the vector case. 相似文献
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Positivity - Let X and Y be locally compact Hausdorff spaces. In this paper we study surjections $$T: A \longrightarrow B$$ between certain subsets A and B of $$C_0(X)$$ and $$C_0(Y)$$ ,... 相似文献
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Quasibarrelled, barrelled and bornological tensor products of locally convex spaces are studied. A device, called the desintegration lemma, is developed for the most difficult case, that of the injective topology. Applications are given to spaces of vector-valued continuous functions.Both authors thank the Volkswagenstiftung and the A. von Humboldt Stiftung. The second author is a research associate of the Belgian National Fund for Scientific Research N.F.W.O. 相似文献
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In this paper we study multilinear isometries defined on certain subspaces of vector-valued continuous functions. We provide conditions under which such maps can be properly represented. Our results contain all known results concerning linear and bilinear isometries defined between spaces of continuous functions. The key result is a vector-valued version of the additive Bishop’s Lemma, which we think has interest in itself. 相似文献
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Let A and B be strongly separating linear subspaces of C0(X) and C0(Y), respectively, and assume that ?A ≠ ?? (?A stands for the set of generalized peak points for A) and ?B ≠ ??. Let T: A × B → C0(Z) be a bilinear isometry. Then there exist a nonempty subset Z0 of Z, a surjective continuous mapping h: Z0 → ?A × ?B and a norm‐one continuous function a: Z0 → K such that T (f, g)(z) = a (z)f (πx (h (z))g (πy (h (z)) for all z ∈ Z0 and every pair (f, g) ∈ A × B. These results can be applied, for example, to non‐unital function algebras (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Jiří Spurný 《Archiv der Mathematik》2017,108(5):473-483
Let X be a simplex with the set \({\text {ext}}\, X\) of extreme points being Lindelöf. We show that a continuous bounded mapping defined on \({\text {ext}}\, X\) with values in a Fréchet space F can be extended to a mapping that is a pointwise limit of a bounded sequence of affine continuous mappings from X to F. 相似文献
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Marcus Carlsson 《Journal of Mathematical Analysis and Applications》2009,354(1):184-201
Let H be a Hilbert space of analytic functions on the unit disc D with ‖Mz‖?1, where Mz denotes the operator of multiplication by the identity function on D. Under certain conditions on H it has been shown by Aleman, Richter and Sundberg that all invariant subspaces have index 1 if and only if for all f∈H, f?0 [A. Aleman, S. Richter, C. Sundberg, Analytic contractions and non-tangential limits, Trans. Amer. Math. Soc. 359 (7) (2007) 3369-3407]. We show that the natural counterpart to this statement in Hilbert spaces of Cn-valued analytic functions is false and prove a correct generalization of the theorem. In doing so we obtain new information on the boundary behavior of functions in such spaces, thereby improving the main result of [M. Carlsson, Boundary behavior in Hilbert spaces of vector-valued analytic functions, J. Funct. Anal. 247 (1) (2007)]. 相似文献