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A strict maximum modulus theorem is proved for certain Banach spaces. As an application it is shown that ifAX=XA * withA hyponormal andX a member of any Schattenp-class withp≥1, thenA * X=XA. 相似文献
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Criteria for nearly strict convexity of Musielak-Orlicz-Bochner function spaces equipped with the Luxemburg norm are given. We also prove that, in Musielak-Orlicz-Bochner function spaces generated by strictly convex Banach space, nearly strict convexity and strict convexity are equivalent. 相似文献
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This paper gives some relations and properties of several kinds of generalized convexity in Banach spaces. As a result, it
proves that every kind of uniform convexity implies the Banach-Sakes property, and several notions of uniform convexity in
literature are actually equivalent. 相似文献
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本文讨论强凸性、L-kR,LωR和(G)性质之间的关系,指出强凸性介于LωR和(G)性质之间,证明光滑的有(G)性质的Banach空间是强凸的,此外指出存在一个Banach空间X,它是LωR但对任意自然数k,X不是L-kR. 相似文献
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Vassilis Kanellopoulos 《Proceedings of the American Mathematical Society》2000,128(9):2725-2733
In this paper two convexity criteria are proven. The first one characterizes compact convex sets in a locally convex space and extends a previous result by G. Aumann, while the second one characterizes closed bounded convex sets with the Radon-Nikodým property in a Banach space.
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Iryna Banakh Taras Banakh Anatolij Plichko Anatoliy Prykarpatsky 《Central European Journal of Mathematics》2012,10(6):2264-2271
We find conditions for a smooth nonlinear map f: U → V between open subsets of Hilbert or Banach spaces to be locally convex in the sense that for some c and each positive ? < c the image f(B ?(x)) of each ?-ball B ?(x) ? U is convex. We give a lower bound on c via the second order Lipschitz constant Lip2(f), the Lipschitz-open constant Lipo(f) of f, and the 2-convexity number conv2(X) of the Banach space X. 相似文献
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The general form of characteristic functionals of Gaussian measures in spaces of type 2 and cotype 2 is found. Under the condition of existence of an unconditional basis this problem is solved for spaces not containing l∞n uniformly. The solution uses the language of absolutely summing operators. For each of mentioned space classes it is shown that the results hold in them only. We consider also the equivalent problems on extension of a weak Gaussian distribution and convergence of Gaussian series. Some limit theorems are formulated. 相似文献
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Hai Yun Zhou 《数学学报(英文版)》2014,30(5):755-766
In this paper, it is shown that there is a gap in the paper [Chidume, C. E., Shahzad, N.: Weak convergence theorems for a finite family of strict pseudo-contractions. Nonlinear Anal., 72, 1257–1265(2010)], consequently, the main results of the paper do not hold in uniformly smooth Banach spaces. Meanwhile, it is also shown that the main results(Lemma 3.4, Theorems 3.5–3.6, 3.8–3.9) in the paper [Cholamjiak, P., Suantai, S.: Weak convergence theorems for a countable family of strict pseudo-contractions in Banach spaces. Fixed Point Theory Appl., 2010, Article ID 632137, 16 pages(2010)] do not hold in Lpfor p 3. Finally, some modified results are presented in the setting of uniformly smooth and uniformly convex Banach spaces which include Lpfor p ≥ 2 as special cases. Furthermore, our arguments are also different from the ones given by the authors above. 相似文献
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In [1], the authors have shown the existence of non-quasireflexive Banach spaces having unique isomorphic preduals. In fact,
certain James-Lindenstrauss’ spaces have this property. In this paper it is shown that there are many such separable spaces.
More precisely, there exist infinitely many different isomorphic types of James-Lindenstrauss’ spaces which are non-quasireflexive
and have unique isomorphic preduals.
The research of both authors was partially supported by N.S.F. Grant No. MPS75-07115 相似文献
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By way of the Bochner integral of vector-valued functions, the integral convexity of sets and functionals and the concept of integral extreme points of sets are introduced in Banach spaces. The relations between integral convexity and convexity are mainly discussed, two integral extreme points theorems and their applications are obtained at last. 相似文献
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Boundedness of the Hardy operator and its adjoint is characterized between Banach function spaces Xq and Lp. By applying a limiting procedure, corresponding boundedness of the geometric mean operator is also derived. 相似文献
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Vitalii Marchenko 《Central European Journal of Mathematics》2014,12(11):1714-1732
We extend a theorem of Kato on similarity for sequences of projections in Hilbert spaces to the case of isomorphic Schauder decompositions in certain Banach spaces. To this end we use ?ψ-Hilbertian and ∞-Hilbertian Schauder decompositions instead of orthogonal Schauder decompositions, generalize the concept of an orthogonal Schauder decomposition to the case of Banach spaces and introduce the class of Banach spaces with Schauder-Orlicz decompositions. Furthermore, we generalize the notions of type, cotype, infratype and M-cotype of a Banach space and study the properties of unconditional Schauder decompositions in Banach spaces possessing certain geometric structure. 相似文献
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Near convexity,near smoothness and approximative compactness of half spaces in Banach spaces
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The authors discuss the dual relation of nearly very convexity and property WS. By two kinds of near convexities and two kinds of near smoothness, the authors prove a series of characterizations such that every half-space in Banach space X and every weak* half-space in the dual space X* are approximatively weakly compact and approximatively compact. They show a sufficient condition such that a Banach space X is a Asplund space. Using upper semi-continuity of duality mapping, the authors also give two characterizations of property WS and property S. 相似文献
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