τ-CHEBYSHEV AND τ-COCHEBYSHEV SUBPSACES OF BANACH SPACES

The concepts of quasi-Chebyshev and weakly-Chebyshev and σ-Chebyshev were defined [3 - 7], andas a counterpart to best approximation in normed linear spaces, best coapprozimation was introduced by Franchetti and Furi^[1]. In this research, we shall define τ-Chebyshev subspaces and τ-cochebyshev subspaces of a Banach space, in which the property τ is compact or weakly-compact, respectively. A set of necessary and sufficient theorems under which a subspace is τ-Chebyshev is defined.     

BOUNDEDNESS OF SEVERAL OPERATORS ON MARTINGALE SPACES AND THE GEOMETRY OF BANACH SPACES

The aim of this paper is establishing some inequalities of several operators on Banach-space-valued martingales and using them to give some characterizations of geometrical properties of Banach spaces. In particular, the Φ-function nequalitities of sharp operators f_p~#, f_p~#, p-variation operators W_p, W_p and the martingale tranform operator T_v are discussed. It is proved that the boundedness of these operators characterizes the smoothness, convexity and UMD-property of Banach spaces.     

CONTINUITY AND LINEARITY OF ADDITIVE DERIVATIONS OF NEST ALGEBRAS ON BANACH SPACES

This paper discusses the problem concerning the continuity and linearity of additive derivation of nest algebras on normed spaces. It is proved that every linear derivation of a nest algebraalgN is continuous provided that one of the following conditions is satisfied: (1) 0 (?) 0. (2)X_ (?) X. (3) there exists a non-trivial idempotent p in algN such that the range of p belongsto N. It is also proved that every additive derivation of a nest algebra is automatically linearif the underlying normed space is infinite dimemnsional.     

ODEs IN BANACH SPACES AND FIXED POINTS OF WEAKLY INWARD MAPS

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DECOMPOSITION OF A CLASS OF FUNCTIONALS AND THE PREDICTABLE REPRESENTATION THEOREM ON BANACH SPACES

Let B be a separable real Banach space and X(t) be a symmetric conservative diffusionprocess taking values in B. In this paper, we decompose the functional u(X(t),t) into a sumof a square integrable martingale and a regular 0-quadratic variation process. On this basis, weestablish the predictable representation theorem of X(t).     

ε-WEAKLY CHEBYSHEV SUBSPACES OF BANACH SPACES

We will define and characterize c-weakly Chebyshev subspaces of Banach spaces. We will prove that all closed subspaces of a Banach space X are ε-weakly Chebyshev if and only if X is reflexive.     

ε-PSEUDO CHEBYSHEV AND ε- QUASI CHEBYSHEV SUBSPACES OF BANACH SPACES

We will define and characterize ε-pseudo Chebyshev and ε-quasi Chebyshev subspaces of Banach spaces. We will prove that a closed subspace W is ε-pseudo Chebyshev if and only if W is ε-quasi Chebyshev.     

ε-PSEUDO CHEBYSHEV AND ε- QUASI CHEBYSHEV SUBSPACES OF BANACH SPACES

We will define and characterize ε-pseudo Chebyshev and ε-quasi Chebyshev subspaces of Banach spaces. We will prove that a closed subspace W is ε-pseudo Chebyshev if and only if W is ε-quasi Chebyshev.     

EXISTENCE OF A NON-STRICT MOPRPHISM OF QUOTIENT BANACH SPACES

Abstract. In this paper we prove the existence of a morphism of quotient Banach spaces that is not strict.     

（1.2） INVERSES OF OPERATORS BETWEEN BANACH SPACES AND LOCAL CONJUGACY THEOREM

1.(1.2)InverseandLocalFinePropertyofaFamilyofOperatorsTxLetEandFbebothBanachspaces,andB(E,F)thesetofallboundedlinearoperatorsfromEintoFAnoperatorT B(F,E)issaidtobea(1.2)inverseofTifTT T=TandT TT =T .IfT satisfiesonlythefirstcondition,thenT issaidtobe...     

BANACH SPACES AND INEQUALITIES ASSOCIATED WITH NEW GENERALIZATION OF CESàRO MATRIX

Let the triangle matrix A^ru be a generalization of the Cesàro matrix and U ∈{c₀,c,l_∞}.In this study,we essentially deal with the space U(A^ru) defined by the domain of A^ru in the space U and give the bases,and determine the K?the-Toeplitz,generalized K?theToeplitz and bounded-duals of the space U(A^ru).We characterize the classes(l_∞(A^ru):l_∞),(l_∞(A^ru):c),(c(A^ru):c),and...     

STABILITY OF A PAIR OF BANACH SPACES FOR ε-ISOMETRIES

A pair of Banach spaces(X, Y) is said to be stable if for every ε-isometry f :X → Y, there exist γ 0 and a bounded linear operator T : L(f) → X with ||T|| ≤α such that ||T f(x)-x|| ≤γε for all x ∈ X, where L(f) is the closed linear span of f(X). In this article, we study the stability of a pair of Banach spaces(X, Y) when X is a C(K) space.This gives a new positive answer to Qian's problem. Finally, we also obtain a nonlinear version for Qian's problem.     

EXISTENCE OF RADIAL LIMITS OF HARMONIC FUNCTIONS IN BANACH SPACES

The following result is established:let X be a Banach space without the Radon-Nikodym property,there exists a uniformly bounded harmonic function f defined onthe open unit disk of C with values in X,such that for almost allθ∈[0,2π],(?)f(re~(iθ))does not exist.     

MULTIVALUED DIFFERENTIAL EQUATIONS IN BANACH SPACES AND THEIR APPLICATIONS

IIntroductionConsider the initial value problemDtL干Au＋1ugi．U＜t＜I,oh山)”w,where A is of of。s(S＋)and F is a multivalued msp．If F is singl。vlued Hiranoti goteistence results for Fbeing compact．Ahmed and Xiang[21 extended Hirano’s results forFsatls州ngthat＜Fu。,u。一U＞－＋ 0 lfunconverges wewyto h;While Liul3]e枕ended theabOV6 th6lltlollsd T6SllltS to COf正erpolldlllg ClAsS Of yatlatlollal ill6qttallt16s ld lfittodllC6d 8 hO16gmerdC0nd让ND th幼劝m比a bro劝0 d%sdpenurb砒…     

A NOTE ON REARRANGEMENTS OF SERIES IN BANACH SPACES

We generalize Kadec‘s and Yan Zikun‘s resuhs in [1],[2] to prove; in every infinite dimensional real Banach space Y there exist an infinite dimensional subspace X and a series ∑xn such that ∑xn has property(N) in X. but(the domain of sums of this series) S(∑xn) is not a convex set.     

THE MAXIMUM AND MINIMUM SOLUTIONS OF NONLINEAR INTEGRODIFFERENTIAL EQUATIONS OF MIXED TYPE WITH IMPULSES IN BANACH SPACES

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REPRESENTATION OF MARTINGALE ADDITIVE FUNCTIONALS 0N BANACH SPACES

Assume that B is a separable real Banach space and X(t) is a diffusion process on B. In thispaper, we will establish the representation theorem of martingale additive functionals of X(t).     

MULTIPLE SOLUTICNS OF NONLINEAR FREDHOLM INTEGRAL EQUATIONS IN BANACH SPACES

In this paper, the author uses the topological degree theory to investigate the multiple solutions of nonlinear Fredholm integral equations in Banach spaces. Two new theorems aro obtained and two examples are given.     

ON THE UNIFORM CONTINUITY OF METRIC PROJECTIONS IN BANACH SPACES

Let M be a convex Chebyshev subset of a uniformly convex and uniformly smoothBanach space.It is proved that the metric projection P_M of X onto M is uniformly continu-ous on every bounded subset of X.Moreover,a global and explicit estimate on the modulus ofcontinuity of the metric projection is obtained.     

ASYMPTOTICALLY ISOMETRIC COPIES OF l_P (1≤P<∞) AND c_0 IN BANACH SPACES

Let X be a Banach space. If there exists a quotient space of X which is asymptotically isometric to l1, then X contains complemented asymptotically isometric copies of l1. Every infinite dimensional closed subspace of l1 contains a complemented subspace of l1 which is asymptotically isometric to l1. Let X be a separable Banach space such that X* contains asymptotically isometric copies of lp (1< p <∞).Then there exists a quotient space of X which is asymptotically isometric to lq (1/p 1/q=1).Complemented asymptotically isometric copies of co in K(X, Y) and W(X, Y) are discussed. Let X be a Gelfand-Phillips space. If X contains asymptotically isometric copies of Co, it has to contain complemented asymptotically isometric copies of Co.