ALMOST TRANSITIVITY IN $\mathcal{C}_0$ SPACES OF VECTOR-VALUED FUNCTIONS

AbstractBy means of $M$-structure and dimension theory, we generalize some known results and obtain some new ones on almost transitivity in $\mathcal{C}_0(L,X)$. For instance, if $X$ has the strong Banach–Stone property, then almost transitivity of $\mathcal{C}_0(L,X)$ is divided into two weaker properties, one of them depending only on topological properties of $L$ and the other being closely related to the covering dimensions of $L$ and $X$. This leads to some non-trivial examples of almost transitive $\mathcal{C}_0(L,X)$ spaces.

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On locally Lipschitz vector-valued invex functions

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700012491 ◽

1993 ◽

Vol 47 (2) ◽

pp. 259-272 ◽

Cited By ~ 10

Author(s):

N.D. Yen ◽

P.H. Sach

Keyword(s):

The Other ◽

Joint Paper ◽

Invex Functions ◽

Locally Lipschitz ◽

Invex Function ◽

Vector Valued Functions ◽

Vector Valued ◽

Class Of Functions

The four types of invexity for locally Lipschitz vector-valued functions recently introduced by T. W. Reiland are studied in more detail. It is shown that the class of restricted K-invex in the limit functions is too large to obtain desired optimisation theorems and the other three classes are contained in the class of functions which are invex 0 in the sense of our previous joint paper with B. D. Craven and T. D. Phuong. We also prove that the extended image of a locally Lipschitz vector-valued invex function is pseudoconvex in the sense of J. Borwein at each of its points.

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Farkas-Type Results for Vector-Valued Functions with Applications

Journal of Optimization Theory and Applications ◽

10.1007/s10957-016-1055-2 ◽

2017 ◽

Vol 173 (2) ◽

pp. 357-390 ◽

Cited By ~ 11

Author(s):

N. Dinh ◽

M. A. Goberna ◽

M. A. López ◽

T. H. Mo

Keyword(s):

Vector Valued Functions ◽

Vector Valued

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Diameter-preserving linear bijections of function spaces

Journal of the Australian Mathematical Society ◽

10.1017/s1446788700002378 ◽

2001 ◽

Vol 70 (3) ◽

pp. 323-336 ◽

Cited By ~ 6

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.

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

Israel Journal of Mathematics ◽

10.1007/bf02937334 ◽

1997 ◽

Vol 98 (1) ◽

pp. 189-207 ◽

Cited By ~ 5

Author(s):

R. DeLaubenfels ◽

Z. Huang ◽

S. Wang ◽

Y. Wang

Keyword(s):

Laplace Transforms ◽

Semigroups Of Operators ◽

Vector Valued Functions ◽

Vector Valued

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

Glasgow Mathematical Journal ◽

10.1017/s0017089514000123 ◽

2014 ◽

Vol 57 (1) ◽

pp. 17-82 ◽

Cited By ~ 2

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.

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Strict Topologies for Vector-Valued Functions

Canadian Journal of Mathematics ◽

10.4153/cjm-1974-079-1 ◽

1974 ◽

Vol 26 (4) ◽

pp. 841-853 ◽

Cited By ~ 24

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].

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