An approximation theorem for vector valued functions

2006 ◽  
pp. 126-137 ◽  
Author(s):  
Yaki Sternfeld ◽  
Yitzhak Weit
Keyword(s):  
Approximation Theorem ◽  
Vector Valued Functions ◽  
Vector Valued

The spectrum and eigenspaces of a meromorphic operator-valued function

1997 ◽  
Vol 127 (5) ◽  
pp. 1027-1051 ◽  
Author(s):  
Robert Magnus
Keyword(s):  
Banach Space ◽  
Riemann Surface ◽  
Spectral Theory ◽  
Approximation Theorem ◽  
Meromorphic Mapping ◽  
Bounded Operators ◽  
Single Operator ◽  
Definition Of ◽  
Vector Valued Functions ◽  
Vector Valued

SynopsisIt is shown how to associate eigenvectors with a meromorphic mapping defined on a Riemann surface with values in the algebra of bounded operators on a Banach space. This generalises the case of classical spectral theory of a single operator. The consequences of the definition of the eigenvectors are examined in detail. A theorem is obtained which asserts the completeness of the eigenvectors whenever the Riemann surface is compact. Two technical tools are discussed in detail: Cauchy-kernels and Runge's Approximation Theorem for vector-valued functions.

scholarly journals Farkas-Type Results for Vector-Valued Functions with Applications

2017 ◽  
Vol 173 (2) ◽  
pp. 357-390 ◽  
Author(s):  
N. Dinh ◽  
M. A. Goberna ◽  
M. A. López ◽  
T. H. Mo
Keyword(s):  
Vector Valued Functions ◽  
Vector Valued

scholarly journals Diameter-preserving linear bijections of function spaces

2001 ◽  
Vol 70 (3) ◽  
pp. 323-336 ◽  
Author(s):  
T. S. S. R. K. Rao ◽  
A. K. Roy
Keyword(s):  
Maximal Ideal ◽  
Convex Set ◽  
Compact Convex ◽  
Extreme Points ◽  
Continuous Functions ◽  
Ideal Space ◽  
Function Algebras ◽  
Compact Convex Set ◽  
Vector Valued Functions ◽  
Vector Valued

AbstractIn this paper we give a complete description of diameter-preserving linear bijections on the space of affine continuous functions on a compact convex set whose extreme points are split faces. We also give a description of such maps on function algebras considered on their maximal ideal space. We formulate and prove similar results for spaces of vector-valued functions.

Laplace transforms of polynomially bounded vector-valued functions and semigroups of operators

1997 ◽  
Vol 98 (1) ◽  
pp. 189-207 ◽  
Author(s):  
R. DeLaubenfels ◽  
Z. Huang ◽  
S. Wang ◽  
Y. Wang
Keyword(s):  
Laplace Transforms ◽  
Semigroups Of Operators ◽  
Vector Valued Functions ◽  
Vector Valued

scholarly journals THE LOCAL NON-HOMOGENEOUS Tb THEOREM FOR VECTOR-VALUED FUNCTIONS

2014 ◽  
Vol 57 (1) ◽  
pp. 17-82 ◽  
Author(s):  
TUOMAS P. HYTÖNEN ◽  
ANTTI V. VÄHÄKANGAS
Keyword(s):  
Singular Integrals ◽  
Local Version ◽  
Square Functions ◽  
Property A ◽  
Martingale Differences ◽  
Umd Spaces ◽  
Function Lattice ◽  
Vector Valued Functions ◽  
Vector Valued ◽  
Similar Extension

AbstractWe extend the local non-homogeneous Tb theorem of Nazarov, Treil and Volberg to the setting of singular integrals with operator-valued kernel that act on vector-valued functions. Here, ‘vector-valued’ means ‘taking values in a function lattice with the UMD (unconditional martingale differences) property’. A similar extension (but for general UMD spaces rather than UMD lattices) of Nazarov-Treil-Volberg's global non-homogeneous Tb theorem was achieved earlier by the first author, and it has found applications in the work of Mayboroda and Volberg on square-functions and rectifiability. Our local version requires several elaborations of the previous techniques, and raises new questions about the limits of the vector-valued theory.

Strict Topologies for Vector-Valued Functions

1974 ◽  
Vol 26 (4) ◽  
pp. 841-853 ◽  
Author(s):  
Robert A. Fontenot
Keyword(s):  
Vector Space ◽  
Topological Vector Space ◽  
Measure Theory ◽  
Strict Topology ◽  
Locally Compact ◽  
Topological Measure ◽  
Topological Measure Theory ◽  
Vector Valued Functions ◽  
Vector Valued ◽  
Locally Compact Hausdorff Space

This paper is motivated by work in two fields, the theory of strict topologies and topological measure theory. In [1], R. C. Buck began the study of the strict topology for the algebra C*(S) of continuous, bounded real-valued functions on a locally compact Hausdorff space S and showed that the topological vector space C*(S) with the strict topology has many of the same topological vector space properties as C0(S), the sup norm algebra of continuous realvalued functions vanishing at infinity. Buck showed that as a class, the algebras C*(S) for S locally compact and C*(X), for X compact, were very much alike. Many papers on the strict topology for C*(S), where S is locally compact, followed Buck's; e.g., see [2; 3].

The greatest regular subalgebra of certain Banach algebras of vector-valued functions

1994 ◽  
Vol 43 (3) ◽  
pp. 435-446
Author(s):  
Robert Kantrowitz ◽  
Michael M. Neumann
Keyword(s):  
Banach Algebras ◽  
Vector Valued Functions ◽  
Vector Valued

scholarly journals Refined limiting imbeddings for Sobolev spaces of vector-valued functions

2005 ◽  
Vol 227 (2) ◽  
pp. 372-388 ◽  
Author(s):  
Miroslav Krbec ◽  
Hans-Jürgen Schmeisser
Keyword(s):  
Sobolev Spaces ◽  
Vector Valued Functions ◽  
Vector Valued

Vector-Valued Functions

2013 ◽  
pp. 209-215
Author(s):  
John Vince
Keyword(s):  
Vector Valued Functions ◽  
Vector Valued

scholarly journals Approximation properties of vector valued functions

1974 ◽  
Vol 53 (1) ◽  
pp. 85-94 ◽  
Author(s):  
Robert Buck
Keyword(s):  
Approximation Properties ◽  
Vector Valued Functions ◽  
Vector Valued
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