Search results for "Banach manifold"

Group-symmetric holomorphic functions on a Banach space

2016

We study the holomorphic functions on a complex Banach space E that are invariant under the action of a given group of operators on E. A great variety of situations occur depending, of course, on the group and the space. Nevertheless, in the examples we deal with, they can be described in terms of a few natural ones and functions of a finite number of variables. Fil: Aron, Richard. Universidad de Valencia; España Fil: Galindo, Pablo. Universidad de Valencia; España Fil: Pinasco, Damian. Universidad Torcuato Di Tella; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina Fil: Zalduendo, Ignacio Martin. Universidad Torcuato Di Tella; Argentina. Consejo Nacional de I…

Tensor products of Fréchet or (DF)-spaces with a Banach space

1992

Abstract The aim of the present article is to study the projective tensor product of a Frechet space and a Banach space and the injective tensor product of a (DF)-space and a Banach space. The main purpose is to analyze the connection of the good behaviour of the bounded subsets of the projective tensor product and of the locally convex structure of the injective tensor product with the local structure of the Banach space.

Gaussian surface measures and the radon transform on separable banach spaces

1980

Homeomorphic graph manifolds: A contribution to the μ constant problem

1999

Abstract We give a characterization, in terms of homological data in covering spaces, of those maps between (3-dimensional) graph manifolds which are homotopic to homeomorphisms. As an application we give a condition on a cobordism between graph manifolds that guarantees that they are homeomorphic. This in turn is applied to give a partial result on the μ -constant problem in (complex) dimension three.

Norm continuity and related notions for semigroups on Banach spaces

1996

We find some conditions on a c0-semigroup on a Banach space and its resolvent connected with the norm continuity of the semigroup. We use them to get characterizations of norm continuous, eventually norm continuous and eventually compact semigroups on Hilbert spaces in terms of the growth of the resolvent of their generator.

Evolution semigroups and time operators on Banach spaces

2010

AbstractWe present new general methods to obtain shift representation of evolution semigroups defined on Banach spaces. We introduce the notion of time operator associated with a generalized shift on a Banach space and give some conditions under which time operators can be defined on an arbitrary Banach space. We also tackle the problem of scaling of time operators and obtain a general result about the existence of time operators on Banach spaces satisfying some geometric conditions. The last part of the paper contains some examples of explicit constructions of time operators on function spaces.

Operator martingale decomposition and the Radon-Nikodym property in Banach spaces

2010

Abstract We consider submartingales and uniform amarts of maps acting between a Banach lattice and a Banach lattice or a Banach space. In this measure-free setting of martingale theory, it is known that a Banach space Y has the Radon–Nikodým property if and only if every uniformly norm bounded martingale defined on the Chaney–Schaefer l-tensor product E ⊗ ˜ l Y , where E is a suitable Banach lattice, is norm convergent. We present applications of this result. Firstly, an analogues characterization for Banach lattices Y with the Radon–Nikodým property is given in terms of a suitable set of submartingales (supermartingales) on E ⊗ ˜ l Y . Secondly, we derive a Riesz decomposition for uniform …

Geometric mean and triangles inscribed in a semicircle in Banach spaces

2008

AbstractWe consider the triangles with vertices x, −x and y where x,y are points on the unit sphere of a normed space. Using the geometric means of the variable lengths of the sides of these triangles, we define two geometric constants for Banach spaces. These constants are closely related to the modulus of convexity of the space under consideration, and they seem to represent a useful tool to estimate the exact values of the James and Jordan–von Neumann constants of some Banach spaces.