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1.
We prove that an order unit can be adjoined to every L
∞-matricially Riesz normed space. We introduce a notion of strong subspaces. The matrix order unit space obtained by adjoining an order unit to an L
∞-matrically Riesz normed space is unique in the sense that the former is a strong L
∞-matricially Riesz normed ideal of the later with codimension one. As an application of this result we extend Arveson’s extension
theorem to L
∞-matircially Riesz normed spaces. As another application of the above adjoining we generalize Wittstock’s decomposition of
completely bounded maps into completely positive maps on C
*-algebras to L
∞-matricially Riesz normed spaces. We obtain sharper results in the case of approximate matrix order unit spaces.
Mathematics Subject Classification (2000). Primary 46L07 相似文献
2.
Stanislav Smirnov 《Acta Mathematica》2010,205(1):189-197
We introduce canonical antisymmetric quasiconformal maps, which minimize the quasiconformality constant among maps sending
the unit circle to a given quasicircle. As an application we prove Astala’s conjecture that the Hausdorff dimension of a k-quasicircle is at most 1+k
2. 相似文献
3.
Curtis T. McMullen 《Geometric And Functional Analysis》2010,20(3):726-740
This paper describes two new types of winning sets in
\mathbbRn{\mathbb{R}^n}, defined using variants of Schmidt’s game. These strong and absolute winning sets include many Diophantine sets of measure zero and first category, and have good behavior under countable intersections.
Most notably, they are invariant under quasiconformal maps, while classical winning sets are not. 相似文献
4.
Armen Glebovich Sergeev 《中国科学A辑(英文版)》2008,51(4):695-706
We study harmonic maps from Riemann surfaces M to the loop spaces ΩG of compact Lie groups G, using the twistor approach. We conjecture that harmonic maps of the Riemann sphere ℂℙ1 into ΩG are related to Yang-Mills G-fields on ℝ4.
This work was partly supported by the RFBR (Grant Nos. 04-01-00236, 06-02-04012), by the program of Support of Scientific
Schools (Grant No. 1542.2003.1), and by the Scientific Program of RAS “Nonlinear Dynamics” 相似文献
5.
In a recent paper, the authors have proved results characterizing convexity-preserving maps defined on a subset of a not-necessarily
finite dimensional real vector space as projective maps. The purpose of this note is three-fold. First, we state a theorem
characterizing continuous, injective, convexity-preserving maps from a relatively open, connected subset of an affine subspace
of ℝ
m
into ℝ
n
as projective maps. This result follows from the more general results stated and proved in a coordinate-free manner in the
above paper, and is intended to be more accessible to researchers interested in optimization algorithms. Second, based on
that characterization theorem, we offer a characterization theorem for collinear scalings first introduced by Davidon in 1977
for deriving certain algorithms for nonlinear optimization, and a characterization theorem for projective transformations
used by Karmarkar in 1984 in his linear programming algorithm. These latter two theorems indicate that Davidon’s collinear
scalings and Karmarkar’s projective transformations are the only continuous, injective, convexity-preserving maps possessing
certain features that Davidon and Karmarkar respectively desired in the derivation of their algorithms. The proofs of these
latter two theorems utilize our characterization of continuous, injective, convexity-preserving maps in a way that has implications
to the choice of scalings and transformations in the derivation of optimization algorithms in general. The third purpose of
this note is to point this out.
Received: January 2000 / Accepted: November 2000?Published online January 17, 2001 相似文献
6.
Alessio Figalli 《Mathematische Annalen》2010,347(1):43-57
In this paper we study the regularity of flow maps of H
3/2-vector fields on the circle in terms of fractional Sobolev spaces. This problem is motivated by the understanding of the
geometry of Bers’s universal Teichmüller space. 相似文献
7.
Jérôme Buzzi 《Israel Journal of Mathematics》1997,100(1):125-161
We generalize the technique of Markov Extension, introduced by F. Hofbauer [10] for piecewise monotonic maps, to arbitrary
smooth interval maps. We also use A. M. Blokh’s [1] Spectral Decomposition, and a strengthened version of Y. Yomdin’s [23]
and S. E. Newhouse’s [14] results on differentiable mappings and local entropy.
In this way, we reduce the study ofC
r
interval maps to the consideration of a finite number of irreducible topological Markov chains, after discarding a small
entropy set. For example, we show thatC
∞ maps have the same properties, with respect to intrinsic ergodicity, as have piecewise monotonic maps. 相似文献
8.
Mihai Cristea 《Complex Analysis and Operator Theory》2011,5(3):863-880
The paper continues the work of Royster (Duke Math J 19:447–457, 1952), Mocanu [Mathematica (Cluj) 22(1):77–83, 1980; Mathematica
(Cluj) 29:49–55, 1987], Cristea [Mathematica (Cluj) 36(2):137–144, 1994; Complex Var 42:333–345, 2000; Mathematica (Cluj)
43(1):23–34, 2001; Mathematica (Cluj), 2010, to appear; Teoria Topologica a Functiilor Analitice, Editura Universitatii Bucuresti,
Romania, 1999] of extending univalence criteria for complex mappings to C
1 mappings. We improve now the method of Loewner chains which is usually used in complex univalence theory for proving univalence
criteria or for proving quasiconformal extensions of holomorphic mappings f : B → C
n
to C
n
. The results are surprisingly strong. We show that the usual results from the theory, like Becker’s univalence criteria remain
true for C
1 mappings and since we use a stronger form of Loewner’s theory, we obtain results which are stronger even for holomorphic
mappings f : B → C
n
. In our main result (Theorem 4.1) we end the researches dedicated to quasiconformal extensions of K-quasiregular and holomorphic mappings f : B → C
n
to C
n
. We show that a C
1 quasiconformal map f : B → C
n
can be extended to a quasiconformal map F : C
n
→ C
n
, without any metric condition imposed to the map f. 相似文献
9.
We give a topological characterization of rational maps with disconnected Julia sets. Our results extend Thurston’s characterization
of postcritically finite rational maps. In place of iteration on Teichmüller space, we use quasiconformal surgery and Thurston’s
original result. 相似文献
10.
A. G. Sergeev 《Journal of Mathematical Sciences》2008,149(5):1608-1617
We study harmonic maps from Riemann surfaces M to the loop spaces ΩG of compact Lie groups G, using the twistor approach. Harmonic maps into loop spaces are of special interest because of their relation to the Yang-Mills
equations on ℝ4.
__________
Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions),
Vol. 16, Differential and Functional Differential Equations. Part 2, 2006. 相似文献
11.
Jouni Luukkainen 《Monatshefte für Mathematik》1991,111(1):35-46
We modify the proof of an earlier result of ours to deforming topological, bi-Lipschitz, and quasiconformal embeddings of an open subsetU ofR
n which now are of small uniform distance from the inclusion map. As an application we show that two bi-Lipschitz homeomorphismsf
0,f
1:R
nRn are bi-Lipschitz isotopic if and only ifd(f
0,f
1)<.Research supported in part by a grant from the Institut Mittag-Leffler. 相似文献
12.
Certain Sobolev spaces of S
1-valued functions can be written as a disjoint union of homotopy classes. The problem of finding the distance between different
homotopy classes in such spaces is considered. In particular, several types of one-dimensional and two-dimensional domains
are studied. Lower bounds are derived for these distances. Furthermore, in many cases it is shown that the lower bounds are
sharp but are not achieved.
The first author’s work of was supported in part by NSF grant 0503887.
The second author’s research of was supported by G.S. Elkin research fund. 相似文献
13.
David Kalaj 《Mathematische Zeitschrift》2008,260(2):237-252
Let Ω and Ω1 be Jordan domains, let μ ∈ (0, 1], and let be a harmonic homeomorphism. The object of the paper is to prove the following results: (a) If f is q.c. and ∂Ω, ∂Ω1 ∈ C
1,μ
, then f is Lipschitz; (b) if f is q.c., ∂Ω, ∂Ω1 ∈ C
1,μ
and Ω1 is convex, then f is bi-Lipschitz; and (c) if Ω is the unit disk, Ω1 is convex, and ∂Ω1 ∈ C
1,μ
, then f is quasiconformal if and only if its boundary function is bi-Lipschitz and the Hilbert transform of its derivative is in
L
∞. These extend the results of Pavlović (Ann. Acad. Sci. Fenn. 27:365–372, 2002).
相似文献
14.
Assaf Libman 《Mathematische Zeitschrift》2007,255(3):515-548
We give a new proof of the Minami–Webb formula for classifying spaces of finite groups by exploiting Symonds’s resolution
of Webb’s conjecture. The methods are applicable to obtain a stable decomposition of Minami’s type for the classifying spaces
of the three exotic p-local finite groups which were introduced by Ruiz and Viruel at the prime 7. We obtain a similar decomposition for the classifying
spaces of a family of exotic p-local finite groups which were constructed by Broto, Levi and Oliver.
The author was supported by the Nuffield Foundation Grant NAL/00735/G. 相似文献
15.
Longzhi Lin 《Journal of Geometric Analysis》2011,21(2):429-454
In this paper, we show a local energy convexity of W
1,2 maps into CAT(K) spaces. This energy convexity allows us to extend Colding and Minicozzi’s width-sweepout construction to produce closed
geodesics in any closed Alexandrov space of curvature bounded from above, which also provides a generalized version of the
Birkhoff-Lyusternik theorem on the existence of non-trivial closed geodesics in the Alexandrov setting. 相似文献
16.
New fixed point results are presented forU
c
k
(X, X) maps in extension type spaces. 相似文献
17.
The authors prove some embedding theorems for Bergman type spaces of functions defined on quasiconformal balls inR
n,n≥2.
This article was processed by the author using the Springer-Verlag TEX mamath marco package 1990 相似文献
18.
We will discuss about the mapping property of Radon transform on L
p
spaces with power weight. It will be shown that the Pitt’s inequality together with the weighted version of Hardy-Littlewood-Sobolev
lemma imply weighted inequality for the Radon transform. 相似文献
19.
Given a bounding class B, we construct a bounded refinement BK(−) of Quillen’s K-theory functor from rings to spaces. As defined, BK(−) is a functor from weighted rings to spaces, and is equipped with a comparison map BK → K induced by “forgetting control.” In contrast to the situation with B-bounded cohomology, there is a functorial splitting BK(−) ≅ K(−)×BK
rel(−) where BK
rel(−) is the homotopy fiber of the comparison map. 相似文献
20.
We prove the differentiability of Lipschitz maps X → V, where X denotes a PI space, i.e. a complete metric measure space satisfying a doubling condition and a Poincaré inequality, and V denotes a Banach space with the Radon–Nikodym Property (RNP). As a consequence, we obtain a bi-Lipschitz nonembedding theorem
for RNP targets. The differentiation theorem depends on a new specification of the differentiable structure for PI spaces
involving directional derivatives in the direction of velocity vectors to rectifiable curves. We give two different proofs
of this, the second of which relies on a new characterization of the minimal upper gradient. There are strong implications
for the infinitesimal structure of PI spaces which will be discussed elsewhere. 相似文献