On Universally Left-stability of ε-Isometry

LetX,Y be two real Banach spaces andε≥0.A map f:X→Y is said to be a standardε-isometry if|f(x)f(y)x y|≤εfor all x,y∈X and with f(0)=0.We say that a pair of Banach spaces(X,Y)is stable if there existsγ0 such that,for every suchεand every standardε-isometry f:X→Y,there is a bounded linear operator T:L(f)≡spanf(X)→X so that T f(x)x≤γεfor all x∈X.X(Y)is said to be universally left-stable if(X,Y)is always stable for every Y(X).In this paper,we show that if a dual Banach space X is universally left-stable,then it is isometric to a complemented w-closed subspace of∞(Γ)for some setΓ,hence,an injective space;and that a Banach space is universally left-stable if and only if it is a cardinality injective space;and universally left-stability spaces are invariant.     

B值随机元阵列的完全收敛性

令｛Ｘ_ｎｊ;１≤ｊ≤ｎ,ｎ≥１｝为行独立对称的Ｂ值随机元阵列     

On vector-valued random Fourier series

Consider a (complex) Banach spaceX, such thatX C_O, and vectors(X _i ) _i ofX. Consider an independent standard normal sequence(g _i ) _i . Then if anX-valued random Fourier series _{|k| n} e ^ikt g _k x _k satisfies

Wold decomposition in Banach spaces

We propose a natural analog of the Wold decomposition in the case of a linear noninvertible isometry V in a Banach space X. We obtain a criterion for the existence of such a decomposition. In a reflective space, this criterion is reduced to the existence of the linear projection P: X → VX with unit norm. Separately, we discuss the problem of the Wold decomposition for the isometry V _φ induced by an epimorphism φ of a compact set H in the space of continuous functions C(H). We present a detailed study of the mapping z → z ^m of the circle |z| = 1 with an integer m ≥ 2.     

Sublattices of the banach envelope of weak

We prove that every separable Banach lattice is lattice isometric to a closed sublattice of the Banach envelope of Weak

     

Approximate fixed point theorems in Banach spaces with applications in game theory

In this paper some new approximate fixed point theorems for multifunctions in Banach spaces are presented and a method is developed indicating how to use approximate fixed point theorems in proving the existence of approximate Nash equilibria for non-cooperative games.     

The Law of Large Numbers and the Ito-Nisio Theorem for Vector Valued Random Fields

Strong convergence results are obtained for vector-valued random fields. Substantial development of Banach-valued random fields and summability results is needed to provide the framework for the major results since many plausible extensions fail for multi-indexed Banach-valued random variables. This development yields general convergence results for random fields in Banach spaces, including an Ito-Nisio theorem and strong laws of large numbers.     

序列空间上的可乘等距与渐进可乘等距

本文证明了（l^βn）的单位球面间的非满等距在一定条件下可被线性等距延拓至全空间。并刻画了l^p（P〉0）上的非满渐进可乘等距算子．     

Approximate amenability is not bounded approximate amenability

We obtain a new criterion sufficient for approximate amenability of Banach algebras, and an associated criterion sufficient for approximate amenability of _c0$c_0$-direct sums of approximately amenable Banach algebras. We use these criteria to give examples of Banach algebras which are approximately amenable, but not boundedly approximately amenable. Thus we answer a question which was open since the year 2004. This is, so to speak, the complementary result to one of our earlier ones in the paper [F. Ghahramani, C.J. Read, Approximate identities in approximate amenability, J. Funct. Anal. 262 (9) (2012) 3929–3945], where we gave examples of boundedly approximately amenable Banach algebras that are not boundedly approximately contractible.     

Deterministic and random coincidence point results for f-nonexpansive maps

Some deterministic and random coincidence theorems for f-nonexpansive maps are obtained. As applications, invariant approximation theorems are derived. Our results unify, extend and complement various known results existing in the literature.     

Almost isometric flat spaces and perturbation-equivalence

We construct two non-isometric closed subsets of the real line which are almost isometric, and show that any similar example in an Euclidean space is essentially one-dimensional. We then define perturbation-equivalence of almost isometric embeddings, and find a rigid closed subset of the line with an almost isometry onto itself which is not a perturbation of the identity. Finally we show that any almost isometry from an Euclidean space to itself is a perturbation of a sequence of isometries.     

Quaternion normed space with isometry group ℤ2

In a finite-dimensional linear space over the quaternion field, we construct a norm with the following property. Any linear isometry is one of the two transformations x ? x and x ? ?x.     

Partially isometric dilations of noncommuting -tuples of operators

Given a row contraction of operators on a Hilbert space and a family of projections on the space that stabilizes the operators, we show there is a unique minimal joint dilation to a row contraction of partial isometries that satisfy natural relations. For a fixed row contraction the set of all dilations forms a partially ordered set with a largest and smallest element. A key technical device in our analysis is a connection with directed graphs. We use a Wold decomposition for partial isometries to describe the models for these dilations, and we discuss how the basic properties of a dilation depend on the row contraction.

     

Generalized notions of amenability, II

This paper continues the investigation of the first two authors begun in part I. It is shown that approximate amenability and approximate contractibility are the same properties, as are uniform approximate amenability and amenability. Bounded approximate contractibility and bounded approximate amenability are characterized by the existence of suitable operator bounded approximate identities for the diagonal ideal. Results are given on Banach sequence algebras, Lipschitz algebras and Beurling algebras, and on the crucial role of approximate identities. A new proof is given for a result due to N. Grønbæk on characterizing of amenability for Beurling algebras.     

Computing the complexity of the relation of isometry between separable Banach spaces

We compute here the Borel complexity of the relation of isometry between separable Banach spaces, using results of Gao, Kechris [2], Mayer‐Wolf [5], and Weaver [8]. We show that this relation is Borel bireducible to the universal relation for Borel actions of Polish groups. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

两个l~p(Г，Е)型空间的单位球面间满等距映射的表现定理及等距延拓

本文得到两个实的l~p(Γ,Ε)型空间单位球面之间满等距映射的表现定理(这里,1≤p＜ ∞,p≠2,E为内积空间),并导出上述映射可延拓为全空间上的实线性等距算子．     

The evolution of the min-min random graph process

We study the following min-min random graph process G=(G₀,G₁,…): the initial state G₀ is an empty graph on n vertices (n even). Further, G_M+1 is obtained from G_M by choosing a pair {v,w} of distinct vertices of minimum degree uniformly at random among all such pairs in G_M and adding the edge {v,w}. The process may produce multiple edges. We show that G_M is asymptotically almost surely disconnected if M≤n, and that for M=(1+t)n, constant, the probability that G_M is connected increases from 0 to 1. Furthermore, we investigate the number X of vertices outside the giant component of G_M for M=(1+t)n. For constant we derive the precise limiting distribution of X. In addition, for n⁻¹ln⁴n≤t=o(1) we show that tX converges to a gamma distribution.     

A^3中曲面的无穷小等距变形

本文讨论了三维仿射空间Ａ＾３中曲面的无穷小等距变形,给出了Ａ＾３中无穷小Ｏ．Ｂｏｎｎｅｔ等距的定义,得到了曲面允许非平凡的无穷小Ｏ．Ｂｏｎｎｅｔ等距变形的一个充要条件。