Search

In this paper, for 1 < p < ∞, the authors show that the coarse ℓp-Novikov conjecture holds for metric spaces with bounded geometry which are coarsely embeddable into a Banach space with Kasparov-Yu's Property (H). [ABSTRACT FROM AUTHOR]

In this paper, by means of Sadovskii fixed point theorem, the authors establish a result concerning the controllability for a class of abstract neutral functional differential systems where the linear part is non-densely defined and satisfies the Hille-Yosida condition. As an application, an example is provided to illustrate the obtained result. [ABSTRACT FROM AUTHOR]

In this paper, the completeness and minimality properties of some random exponential system in a weighted Banach space of complex functions continuous on the real line for convex nonnegative weight are studied. The results may be viewed as a probabilistic version of Malliavin's classical results. [ABSTRACT FROM AUTHOR]

This paper presents a type of variational principles for real valued w* lower semicontinuous functions on certain subsets in duals of locally convex spaces, and resolve a problem concerning differentiability of convex functions on general Banach spaces. They are done through discussing differentiability of convex functions on nonlinear topological spaces and convexification of nonconvex functions on topological linear spaces. [ABSTRACT FROM AUTHOR]

In this paper, the sharp distortion theorems of the Fréchet-derivative type for a subclass of biholomorphic mappings which have a parametric representation on the unit ball of complex Banach spaces are established, and the corresponding results of the above generalized mappings on the unit polydisk in C are also given. Meanwhile, the sharp distortion theorems of the Jacobi determinant type for a subclass of biholomorphic mappings which have a parametric representation on the unit ball with an arbitrary norm in C are obtained, and the corresponding results of the above generalized mappings on the unit polydisk in C are got as well. Thus, some known results in prior literatures are generalized. [ABSTRACT FROM AUTHOR]

In this paper, the author studies the coarse embedding into uniformly convex Banach spaces. The author proves that the property of coarse embedding into Banach spaces can be preserved under taking the union of the metric spaces under certain conditions. As an application, for a group G strongly relatively hyperbolic to a subgroup H, the author proves that B( n) = { g ∈ G | | g| ≤ n} admits a coarse embedding into a uniformly convex Banach space if H does. [ABSTRACT FROM AUTHOR]

The functional dimension of countable Hilbert spaces has been discussed by some authors. They showed that every countable Hilbert space with finite functional dimension is nuclear. In this paper the authors do further research on the functional dimension, and obtain the following results: (1) They construct a countable Hilbert space, which is nuclear, but its functional dimension is infinite. (2) The functional dimension of a Banach space is finite if and only if this space is finite dimensional. (3) Let B be a Banach space, B* be its dual, and denote the weak * topology of B* by σ(B*, B). Then the functional dimension of (B*,σ(B*, B)) is 1. By the third result, a class of topological linear spaces with finite functional dimension is presented. [ABSTRACT FROM AUTHOR]

The Moore–Penrose metric generalized inverse T[sup +] of linear operator T in Banach space is systematically investigated in this paper. Unlike the case in Hilbert space, even T is a linear operator in Banach Space, the Moore-Penrose metric generalized inverse T[sup +] is usually homogeneous and nonlinear in general. By means of the methods of geometry of Banach Space, the necessary and sufficient conditions for existence, continuity, linearity and minimum property of the Moore-Penrose metric generalized inverse T[sup +] will be given, and some properties of T[sup +] will be investigated in this paper. [ABSTRACT FROM AUTHOR]

In this paper, the author at first develops a method to study convergence of the cascade algorithm in a Banach space without stable assumption on the initial (see Theorem 2.1), and then applies the previous result on the convergence to characterizing compactly supported refinable distributions in fractional Sobolev spaces and Hölder continuous spaces (see Theorems 3.1, 3.3, and 3.4). Finally the author applies the above characterization to choosing appropriate initial to guarantee the convergence of the cascade algorithm (see Theorem 4.2). [ABSTRACT FROM AUTHOR]

Let R be a hyperbolic Riemann surface of conformal infinite type. Denote by A the Banach space of all integrable holomorphic quadratic differentials on R, and by B[sub 0] and B the predual and dual of A, respectively. This paper gives a complete description of the convexity of these three spaces. [ABSTRACT FROM AUTHOR]

This paper investigates the maximal and minimal solutions of initial value problem for n-th order nonlinear integro-differential equations of Volterra type on an infinite interval in a Banach space by establishing a comparison result and using the monotone iterative technique. [ABSTRACT FROM AUTHOR]

The authors establish the coefficient inequalities for a class of holomorphic mappings on the unit ball in a complex Banach space or on the unit polydisk in ℂn, which are natural extensions to higher dimensions of some Fekete and Szegö inequalities for subclasses of the normalized univalent functions in the unit disk. [ABSTRACT FROM AUTHOR]

The free boundary value problems for elliptic differential-operator equations are studied. Several conditions for the uniform maximal regularity with respect to boundary parameters and the Fredholmness in abstract L-spaces are given. In application, the nonlocal free boundary problems for finite or infinite systems of elliptic and anisotropic type equations are studied. [ABSTRACT FROM AUTHOR]

The author establishes operator-valued Fourier multiplier theorems on multi-dimensional Hardy spaces H( $$ \mathbb{T} $$; X), where 1 ≤ p < ∞, d ∈ ℕ, and X is an AUMD Banach space having the property ( α). The sufficient condition on the multiplier is a Marcinkiewicz type condition of order 2 using Rademacher boundedness of sets of bounded linear operators. It is also shown that the assumption that X has the property ( α) is necessary when d ≥ 2 even for scalar-valued multipliers. When the underlying Banach space does not have the property ( α), a sufficient condition on the multiplier of Marcinkiewicz type of order 2 using a notion of d-Rademacher boundedness is also given. [ABSTRACT FROM AUTHOR]

Let B be the unit ball in a complex Banach space. Let S ( B) be the family of normalized starlike mappings f on B such that z = 0 is a zero of order k+1 of f( z)- z. The authors obtain sharp growth and covering theorems, as well as sharp coefficient bounds for various subsets of S ( B). [ABSTRACT FROM AUTHOR]

The authors prove that every complex Banach space admits an equivalent real norm that is far away from being a complex norm. Furthermore, this real norm can be chosen to share many properties with complex norms, but it is still not a complex norm. [ABSTRACT FROM AUTHOR]

It is shown that an n × n matrix of continuous linear maps from a pro- C *-algebra A to L( H), which verifies the condition of complete positivity, is of the form [ V * T ij Φ( · ) V], where Φ is a representation of A on a Hilbert space K, V is a bounded linear operator from H to K, and [ T ij ] is a positive element in the C *-algebra of all n × n matrices over the commutant of Φ( A) in L( K). This generalizes a result of C. Y. Suen in Proc. Amer. Math. Soc., 112(3), 1991, 709–712. Also, a covariant version of this construction is given. [ABSTRACT FROM AUTHOR]

This study focuses on the anisotropic Besov-Lions type spaces B (Ω; E 0, E) associated with Banach spaces E 0 and E. Under certain conditions, depending on l = ( l 1, l 2,⋯, l n ) and α = (α1, α2, ⋯, α n ), the most regular class of interpolation space E α between E 0 and E are found so that the mixed differential operators D α are bounded and compact from B (Ω; E 0, E) to B (Ω; E α). These results are applied to concrete vector-valued function spaces and to anisotropic differential-operator equations with parameters to obtain conditions that guarantee the uniform B separability with respect to these parameters. By these results the maximal B-regularity for parabolic Cauchy problem is obtained. These results are also applied to infinite systems of the quasi-elliptic partial differential equations and parabolic Cauchy problems with parameters to obtain sufficient conditions that ensure the same properties. [ABSTRACT FROM AUTHOR]

Let f : U(x0) ⊂ E → F be a C¹ map and f¹ (x0) be the Frechet derivative of f at x0. In local analysis of nonlinear functional analysis, implicit function theorem, inverse function theorem, local surjectivity theorem, local injectivity theorem, and the local conjugacy theorem are well known. Those theorems are established by using the properties: f1 (x0) is double splitting and R(f¹ (x)) ∩ N(T0+) = {0} near x0. However, in infinite dimensional Banach spaces, f¹(x0) is not always double splitting (i.e., the generalized inverse of f¹(x0) does not always exist), but its bounded outer inverse of f¹(x0) always exists. Only using the C¹ map f and the outer inverse T0# of f¹ (x0), the authors obtain two quasi-local conjugacy theorems, which imply the local conjugacy theorem if x0 is a locally fine point of f. Hence the quasi-local conjugacy theorems generalize the local conjugacy theorem in Banach spaces. [ABSTRACT FROM AUTHOR]