The finite-dimensional decomposition property in non-Archimedean Banach spaces

A non-Archimedean Banach space has the orthogonal finite-dimensional decomposition property（OFDDP） if it is the orthogonal direct sum of a sequence of finite-dimensional subspaces.This property has an influence in the non-Archimedean Grothendieck＇s approximation theory,where an open problem is the following： Let E be a non-Archimedean Banach space of countable type with the OFDDP and let D be a closed subspace of E.Does D have the OFDDP？ In this paper we give a negative answer to this question; we construct a Banach space of countable type with the OFDDP having a one-codimensional subspace without the OFDDP.Next we prove that,however,for certain classes of Banach spaces of countable type,the OFDDP is preserved by taking finite-codimensional subspaces.     

Absolutely summing multipliers on abstract Hardy spaces

We study summing multipliers from Banach spaces of analytic functions on the unit disc of the complex plane to the complex Banach sequence lattices. The domain spaces are abstract variants of the classical Hardy spaces generated by the complex symmetric spaces. Applying interpolation methods, we prove the Hausdorff Young and Hardy-Littlewood type theorems. We show applications of these results to study summing multipliers from the Hardy-Orlicz spaces to the Orlicz sequence lattices. The obtained results extend the well-known results for the Hp spaces.     

THE CODIMENSION FORMULA ON QUASI-INVARIANT SUBSPACES OF THE FOCK SPACE

Let M be an approximately finite codimensional quasi-invariant subspace of the Fock space. This paper gives a formula to calculate the codimension of such spaces and uses this formula to study the structure of quasi-invariant subspaces of the Fock space. Especially, as one of applications, it is showed that the analogue of Beurling's theorem is not true for the Fock space L_a~2 in the case of n > 2.     

Isometric immersions into warped product spaces

This paper concerns the submanifold geometry in the ambient space of warped productmanifolds F^n×σ R, this is a large family of manifolds including the usual space forms R^m, S^m and H^m. We give the fundamental theorem for isometric immersions of hypersurfaces into warped product space R^n×σ R, which extends this kind of results from the space forms and several spaces recently considered by Daniel to the cases of infinitely many ambient spaces.     

The generalized regular points and narrow spectrum points of bounded linear operators on Hilbert spaces

In this paper, we introduce the concepts of generalized regular points and narrow spectrum points of bounded linear operators on Hilbert spaces. The concept of generalized regular points is an extension of the concept regular points, and so, the set of all spectrum points is reduced to the narrow spectrum. We present not only the same and different properties of spectrum and of narrow spectrum but also show the relationship between them. Finally, the well known problem about the invariant subspaces of bounded linear operators on separable Hilbert spaces is simplified to the problem of the operator with narrow spectrum only.     

THE DISTANCE BETWEEN DIFFERENT COMPONENTS OF THE UNIVERSAL TEICHMULLER SPACE

The model of the universal Teichmuller space by the derivatives of logarithm is the union of infinite disconnected components. In this paper, it is proved that the distance between different components is 0, and the distance from the center of a component to every other component is 2.     

The Approach to the Covariance of the Outer Producter of Two Independent Random Vector in Inter Productor Space

The purpose of this article is to prescnt by using vector space methods. a formula as how to calculate the covariance of the outer product of two independent random vecters in inter product space and to makes a discussion on the covariance of the orthogonally invariant random vector and that of the weakly spherically distributed orter produt.     

g-Besselian frames in Hilbert spaces

In this paper, we introduce the concept of a g-Besselian frame in a Hilbert space and discuss the relations between a g-Besselian frame and a Besselian frame. We also give some characterizations of g-Besselian frames. In the end of this paper, we discuss the stability of g-Besselian frames. Our results show that the relations and the characterizations between a g-Besselian frame and a Besselian frame are different from the corresponding results of g-frames and frames.     

INTERPOLATION SPACES BETWEEN H^1 AND L^∞ ON SPACES OF HOMOGENEOUS TYPE

Using the maximal function characterization of Hardy spaces,we study the interpolation spaces between H^1 and L^∞on spaces of homogeneous type.     

Compactness of Composition Operators from the Bloch Space B to QK Spaces

Suppose that φ is an analytic self-map of the unit disk Δ. We consider compactness of the composition operator Cφ from the Bloch space B into the spaces QK defined by a nonnegative, nondecreasing function K（r） for 0 ≤ r 〈 Cφ. Our compactness condition depends only on Φ which can be considered as a slight improvement of the known results. The compactness of Cφ from the Dirichlet space D into the spaces QK is also investigated,     

A Unified Fixed Point Theory in Generalized Convex Spaces

Let B be the class of ＇better＇ admissible multimaps due to the author. We introduce new concepts of admissibility （in the sense of Klee） and of Klee approximability for subsets of G-convex uniform spaces and show that any compact closed multimap in B from a G-convex space into itself with the Klee approximable range has a fixed point. This new theorem contains a large number of known results on topological vector spaces or on various subclasses of the class of admissible G-convex spaces. Such subclasses are those of O-spaces, sets of the Zima-Hadzic type, locally G-convex spaces, and LG-spaces. Mutual relations among those subclasses and some related results are added.     

The hyperspace of the regions below continuous maps with the fell topology

For a Tychonoff space X,we use ↓USC F(X) and ↓C F(X) to denote the families of the hypographs of all semi-continuous maps and of all continuous maps from X to I = [0,1] with the subspace topologies of the hyperspace Cld F(X × I) consisting of all non-empty closed sets in X × I endowed with the Fell topology.In this paper,we shall show that there exists a homeomorphism h:↓USC F(X) → Q = [1,1] ω such that h(↓CF(X))=c0 = {(xn)∈Q| lim n→∞ x n = 0} if and only if X is a locally compact separable metrizable space and the set of isolated points is not dense in X.     

Some Applications of Besov Spaces on Fractals

Let F be a compact d-set in R^n with 0 〈 d ≤ n, which includes various kinds of fractals. The author establishes an embedding theorem for the Besov spaces Bpq^s（F） of Triebel and the Sobolev spaces W^1,P（F,d,μ） of Hajtasz when s 〉 1, 1 〈 p 〈∞ and 0 〈 q ≤ ∞. The author also gives some applications of the estimates of the entropy numbers in the estimates of the eigenvalues of some fractal pseudodifferential operators in the spaces Bpq^0（F） and Fpq^0（F）.     

Distributional Dimension of Fraetal Sets in Local Fields

The distributional dimension of fractal sets in R^n has been systematically studied by Triebel by virtue of the theory of function spaces. In this paper, we first discuss some important properties about the B-type spaces and the F-type spaces on local fields, then we give the definition of the distributional dimension dimD in local fields and study the relations between distributional dimension and Hausdorff dimension. Moreover, the analysis expression of the Hausdorff dimension is given. Lastly, we define the Fourier dimension in local fields, and obtain the relations among all the three dimensions. Keywords local field, B-type space, F-type space, distributional dimension, Hausdorff dimension Fourier dimension     

Bilinear Operators on Herz-type Hardy Spaces on Locally Compact Vilenkin Groups

Let G be a locally compact Vilenkin group. In this paper the authors study the boundedness of bilinear operators B（f, g） given by finite sums of products of Calderdn-Zygmund operators in Herz space and Herz-type Hardy space on G. And an example, the boundedness from the products of Herz space to Herz-type Hardy space is given in the last section.     

On the Extension of Isometries between Unit Spheres of E and C（Ω）

In this paper,we study the extension of isometries between the unit spheres of some Banach spaces E and the spaces C(Ω). We obtain that if the set sm.S1(E) of all smooth points of the unit sphere S1(E) is dense in S1(E),then under some condition,every surjective isometry V0 from S1(E) onto S1(C(Ω)) can be extended to be a real linearly isometric map V of E onto C(Ω).From this resultwe also obtain some corollaries. This is the first time we study this problem on different typical spaces,and the method of proof is also very different too.     

On copositive approximation in some classical spaces of sequences

In this paper the author writes a simple characterization for the best copositive approximation in c; the space of convergent sequences, by elements of finite dimensional Chebyshev subspaces, and shows that it is unique.     

DOMAIN OF THE DOUBLE SEQUENTIAL BAND MATRIX B（r,s） ON SOME MADDOX＇S SPACES

The domain of generalized difference matrix B(r, s) in the classical spaces l∞,c, and c0 was recently studied by Kirisci and Bassar in [16]. The main goal of this article is to introduce the paranormed sequence spaces l∞( B, p), c( B, p), and c0( B, p), which are more general and comprehensive than the corresponding consequences of the matrix domain of B(r, s), as well as other studies in literature. Besides this, the alpha-, beta-, and gamma-duals of the spaces l∞( B, p), c( B, p), and c0( B, p) are computed and the bases of the spaces c( B, p)and c0( B, p) are constructed. The final section of this article is devoted to the characterization of the classes(λ( B, p) :) and( : λ( B, p)), where λ∈ {c, c0, l∞}and is any given sequence space. Additionally, the characterization of some other classes which are related to the space of almost convergent sequences is obtained by means of a given lemma.     

HOLDITCH THEOREM FOR THE CLOSED SPACE CURVES IN LORENTZIAN 3-SPACE

In this article, we give the area formula of the closed projection curve of a closed space curve in Lorentzian 3-space L3. For the 1-parameter closed Lorentzian space motion in L3, we obtain a Holditch Theorem taking into account the Lorentzian matrix multiplication for the closed space curves by using their othogonal projections onto the Euclidean plane in the fixed Lorentzian space. Moreover, we generalize this Holditch Theorem for noncollinear three fixed points of the moving Lorentzian space and any other fixed point on the plane which is determined by these three fixed points.     

Gromov Hyperbolicity of Riemann Surfaces

We study the hyperbolicity in the Gromov sense of Riemann surfaces. We deduce the hyperbolicity of a surface from the hyperbolicity of its ＂building block components＂. We also prove the equivalence between the hyperbolicity of a Riemann surface and the hyperbolicity of some graph associated with it. These results clarify how the decomposition of a Riemann surface into Y-pieces and funnels affects the hyperbolicity of the surface. The results simplify the topology of the surface and allow us to obtain global results from local information.