Characterizations of K-smooth Spaces and K-strongly Smooth Spaces

Some necessary and sufficient conditions for a Banach space to be K-smooth or Kstrongly smooth are obtained.     

Angles of Norm ed Linear Spaces and Characterizations of Inner Product Spaces

§１．　Ｄｅｆｉｎｉｔｉｏｎｓ，ＬｅｍｍａｓａｎｄＴｈｅｏｒｅｍＤｅｆｉｎｉｔｉｏｎ１［１］　Ｌｅｔ（Ｘ，ｙ·ｙ）ｂｅａｒｅａｌｎｏｒｍｅｄｌｉｎｅａｒｓｐａｃｅｏｆｄｅｍｅｎｓｉｏｎｇｒｅａｔｅｒｔｈａｎ１，ｗｅｄｅｆｉｎｅａｎｇｌｅｓＡｍ，ｎ（ｘ，ｙ）ｂｅｔｗｅｅｎｎｏｎｚｅｒｏｖｅｃｔｏｒｓｘａｎｄｙｉｎＸｂｙＡｍ，ｎ（ｘ，ｙ）＝ｃｏｓ－１ｎｙｘｙｘｙ＋ｙｙｙｙｙ２－ｍｙｘｙｘｙ－ｙｙｙｙｙ２＋２（ｍ－ｎ）２（ｍ＋ｎ），ｈｅｒｅｍａｎｄｎａｒｅｔｗｏｎｏｎ－ｎｅｇｅｎｔｉｖｅｉｎｔｅ－ｇｅ…     

Duals of Hardy Spaces of B-valued Martingales for 0<r≤1

The dual of B-valued martingale Hardy space Hs(p)r(B) with small index 0 r ≤ 1,which is associated with the conditional p-variation of B-valued martingale,is characterized.In order to obtain the results,a new type of Campanato spaces for B-valued martingales is introduced and the classical technique of atomic decompositions is improved.Some results obtained here are connected closely with the p-uniform smoothness and q-uniform convexity of the underlying Banach space.     

Exact Calculation of Sums of the Lorentz Spaces Λ<Superscript>α</Superscript> and Applications

The norm on the sum of Lorentz spaces endowed with norms equal to the products of the classical norm by some numbers is exactly calculated. The obtained result makes it possible to prove an extrapolation theorem for collections of Lorentz, Lebesgue, and Marcinkiewicz spaces with a sharp constant.     

Vector Spaces of Non-measurable Functions

We show that there exists an infinite dimensional vector space every non-zero element of which is a non-measurable function. Moreover, this vector space can be chosen to be closed and to have dimensionβ for any cardinalityβ. Some techniques involving measure theory and density characters of Banach spaces are used.     

A Construction of Co-H Spaces

ＡＣｏｎｓｔｒｕｃｔｉｏｎｏｆＣｏ－ＨＳｐａｃｅｓＷａｎｇＸｕ（王旭）（Ｉｎｓｔ．ｏｆＭａｔｈ．，ＡｃａｄｅｍｉｃａＳｉｎｉｃａ，北京，１０００８０）ＣｏｍｍｕｎｉｃａｔｅｄｂｙＳｈｅｎＸｉｎｙａｏＲｅｃｅｉｖｅｄＯｃｔ．１３，１９９４ＡＣｏｎｓｔｒ...     

Covering Spaces of Graphlike Manifolds

ＣｏｖｅｒｉｎｇＳｐａｃｅｓｏｆＧｒａｐｈｌｉｋｅＭａｎｉｆｏｌｄｓ￥ＬｕｉＹａｘｉｎｇ（ＵｎｉｖｅｒｓｉｔｙｏｆＨｅｎａｎ，Ｋａｉｆｅｎｇ，４７５００１）（刘亚星）ＬｅｔＭｂｅｔｈｅｇｒａｐｈｌｉｋｅｍａｎｉｆｏｌｄｏｂｔａｉｎｅｄｂｙｉｄｅｎｔｉ...     

Linear Isometries of S~p Spaces

Abstract This paper gencralizes the result about linear isometries of S~ spaces given by W.P.Novingerand D.M.Oberlin[2]for the unite dise of C to the bounded symmetric domains of C~n     

Perfect Preimages of Some Spaces

ＰｅｒｆｅｃｔＰｒｅｉｍａｇｅｓｏｆＳｏｍｅＳｐａｃｅｓ￥（林寿）ＬｉｎＳｎｏｕ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＮｉｎｇｄｅＴｅａｃｈｅｒｓ＇Ｃｏｌｌｅｇｅ，Ｎｉｎｇｌｅ，Ｆｕｊｉｎａ，３５２１００）Ａｂｓｔｒａｃｔ：ＩｎｔｈｉｓＰ...     

Equivalence of Self-similar and Pseudo-self-similar Tiling Spaces in ℝ<Superscript>2</Superscript>

Given a tiling T, one may form a related tiling, called the derived Voronoi tiling of T, based on a patch of tiles in T. Similarly, for a tiling space X, one can identify a patch which appears regularly in all tilings in X, and form a derived Voronoi space of tilings, based on that patch.     

Function Spaces on τ-Corson Compacta and Tightness of Polyadic Spaces

We apply the general theory of -Corson Compact spaces to remove an unnecessary hypothesis of zero-dimensionality from a theorem on polyadic spaces of tightness . In particular, we prove that polyadic spaces of countable tightness are Uniform Eberlein compact spaces.     

Embedding of Möbius Invariant Function Spaces into Tent Spaces

On the unit disk we introduce a new class of tent spaces \(T^q_{s,t}(\mu )\) for any positive Borel measure \(\mu \), consider a class of Möbius invariant spaces \(Z_p\) of analytic functions, and show that \(Z_p\) is contained in \(T^1_{p,1}\) if and only if \(\mu \) is a p-Carleson measure. This could be considered a continuation or variation of the work initiated by Xiao (Adv Math 217:2075–2088, 2008).     

Volume of Domains in Symmetric Spaces

The authors derive a formula for the volume of a compact domain in a symmetric space from normal sections through a special submanifold in the symmetric space.This formula generalizes the volume of classical domains as tubes or domains given as motions along the submanifold.Finally,some stereological considerations regarding this formula are provided.     

Weakly Sequential Completeness of Orlicz Spaces

Banach space X is called to be weakly sequential complete space, if foreach weak Cauchy Sequence {x_n} in X, there exists a element in X such that x_n→x (n→∞). Weakly sequential completeness in close relationship with refrexivity、separability、weak convexity、bases and isomorphic subspaces in Banach spaces.     

On σ-images of Metric Spaces

In this paper the relation between the σ-images of metrical spaces and spaces with σ-locally finite cs-network, or spaces with σ-locally finite cs^*-network, or spaces with σ-locally finite sequence neighborhood network, or spaces with σ-locally finite sequence open network are established by use of σ-mapping.     

Involutions Fixing Products of Projective Spaces

§１．ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔ（Ｍｎ，Ｔ）ｂｅａｓｍｏｏｔｈｉｎｖｏｌｕｔｉｏｎｏｎａｃｌｏｓｅｄｎ－ｄｉｍｅｎｓｉｏｎａｌｍａｎｉｆｏｌｄ．ＷｅｕｓｅＦｔｏｄｅｎｏｔｅｔｈｅｓｅｔｏｆｐｏｉｎｔｓｆｉｘｅｄｂｙＴ．Ｔｈｅｆｏｌｏｗｉｎｇｑｕｅ...     

On S Points of Orlicz Spaces

We give a criterion for S points and by it we provide a sufficient and necessarycondition for S property of Orlicz spaces.     

Smoothness and Differentiability of Orlicz Spaces

Smoothness and Differentiability of Orlicz spaces are of importance in applications of the approximation theory, the conditional expectation theory, probability limit theorems and the. nonlinear prediction theory as well as in other applications. They are discussed by Rao. M. M. in many parpers, but there     

Geometry and Topology of Spaces of Quasi-constant Curvature

§１．ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＮｎｂｅａｎｎ（≥３）－ｄｉｍｅｎｓｉｏｎａｌＲｉｅｍａｎｎｉａｎｍａｎｉｆｏｌｄ，Ｘ∈ＴｘＮａｎｄＣ（Ｘ，θ）＝｛２－ｐｌａｎｅσＴｘＮ；ｔｈｅａｎｇｌｅｂｅｔｗｅｅｎσａｎｄＸｉｓθ｝．（１．１）Ｉｎ１９７８...     

Elementary transformations and the rationality of the Moduli Spaces of Vector Bundles on ℙ<Superscript>2</Superscript>

In this work, using elementary transformations and prioritary sheaves, we establish birational maps between certain moduli spaces of stable vector bundles over ² with the same rank and different Chern classes. As an application we give a simple proof of the rationality of the moduli spaces M(r; c ₁, c ₂) of rank r stable vector bundles over ² with given Chern classes for a huge families of the triples (r; c ₁, c ₂).Partially supported by BFM2001-3584 Mathematics Subject Classification (2000):Primary 14D20, 14D05; Secondary 14F05