scholarly journals A characterization of cone-convex vector-valued functions

2016 ◽  
Vol 32 (1) ◽  
pp. 79-85
Author(s):  
DAISHI KUROIWA ◽  
◽  
NICOLAE POPOVICI ◽  
MATTEO ROCCA ◽  
◽  
...  
Keyword(s):  
Linear Space ◽  
Convex Analysis ◽  
Linear Functional ◽  
Partially Ordered ◽  
Vector Valued Functions ◽  
Vector Valued

An interesting result in convex analysis, established by J.-P. Crouzeix in 1977, states that a real-valued function defined on a linear space is convex if and only if each function obtained from it by adding a linear functional is quasiconvex. The aim of this paper is to extend this result for vector-valued functions taking values in a partially ordered linear space.

scholarly journals Multipliers of Modules of Continuous Vector-Valued Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Liaqat Ali Khan ◽  
Saud M. Alsulami
Keyword(s):  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Normed Spaces ◽  
Locally Compact ◽  
Continuous Vector ◽  
Vector Valued Functions ◽  
Vector Valued ◽  
Locally Compact Hausdorff Space ◽  
Locally Convex

In 1961, Wang showed that ifAis the commutativeC*-algebraC0(X)withXa locally compact Hausdorff space, thenM(C0(X))≅Cb(X). Later, this type of characterization of multipliers of spaces of continuous scalar-valued functions has also been generalized to algebras and modules of continuous vector-valued functions by several authors. In this paper, we obtain further extension of these results by showing thatHomC0(X,A)(C0(X,E),C0(X,F))≃Cs,b(X,HomA(E,F)),whereEandFarep-normed spaces which are also essential isometric leftA-modules withAbeing a certain commutativeF-algebra, not necessarily locally convex. Our results unify and extend several known results in the literature.

scholarly journals A characterization of quasiconvex vector-valued functions

2002 ◽  
Vol 131 (4) ◽  
pp. 1109-1113 ◽  
Author(s):  
Joël Benoist ◽  
Jonathan M. Borwein ◽  
Nicolae Popovici
Keyword(s):  
Vector Valued Functions ◽  
Vector Valued

scholarly journals BANACH SPACES OF CONTINUOUS VECTOR-VALUED FUNCTIONS OF ORDINALS

2001 ◽  
Vol 44 (1) ◽  
pp. 49-62 ◽  
Author(s):  
Elói Medina Galego
Keyword(s):  
Banach Spaces ◽  
Continuum Hypothesis ◽  
Ordinal Number ◽  
Supremum Norm ◽  
Vector Valued Functions ◽  
Isomorphic Classification ◽  
Vector Valued ◽  
The Continuum

AbstractLet $X$ be a Banach space and $\xi$ an ordinal number. We study some isomorphic classifications of the Banach spaces $X^\xi$ of the continuous $X$-valued functions defined in the interval of ordinals $[1,\xi]$ and equipped with the supremum norm. More precisely, first we use the continuum hypothesis to give an isomorphic classification of $C(I)^\xi$, $\xi\geq\omega_1$. Then we present a characterization of the separable Banach spaces $X$ that are isomorphic to $X^\xi$, $\forall\xi$, $\omega\leq\xi lt \omega_1$. Finally, we show that the isomorphic classifications of $(C(I)\oplus F^*)^\xi$ and $\ell_\infty(\N)^\xi$, where $F$ is the space of Figiel and $\omega\leq\xi lt \omega_1$ are similar to that of $\R^\xi$ given by Bessaga and Pelczynski.AMS 2000 Mathematics subject classification: Primary 46B03; 46B20; 46E15

scholarly journals Spectral Transformations and Associated Linear Functionals of the First Kind

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 107
Author(s):  
Juan Carlos García-Ardila ◽  
Francisco Marcellán
Keyword(s):  
Orthogonal Polynomials ◽  
Linear Space ◽  
Linear Functional ◽  
Linear Functionals ◽  
Spectral Transformations ◽  
Christoffel Transformation ◽  
Complex Coefficients

Given a quasi-definite linear functional u in the linear space of polynomials with complex coefficients, let us consider the corresponding sequence of monic orthogonal polynomials (SMOP in short) (Pn)n≥0. For a canonical Christoffel transformation u˜=(x−c)u with SMOP (P˜n)n≥0, we are interested to study the relation between u˜ and u(1)˜, where u(1) is the linear functional for the associated orthogonal polynomials of the first kind (Pn(1))n≥0, and u(1)˜=(x−c)u(1) is its Christoffel transformation. This problem is also studied for canonical Geronimus transformations.

A macroscopic theory of microcrack growth in brittle materials

1991 ◽  
Vol 335 (1639) ◽  
pp. 455-485 ◽  
Keyword(s):  
Crack Growth ◽  
Brittle Materials ◽  
Macroscopic Theory ◽  
Rate Of Increase ◽  
Inelastic Behaviour ◽  
Constitutive Response ◽  
Macroscopic Plasticity ◽  
Microcrack Growth ◽  
Vector Valued

This paper is concerned with the development of a macroscopic theory of crack growth in fairly brittle materials. Average characteristics of the cracks are described in terms of an additional vector-valued variable in the macroscopic theory, which is determined by an additional momentum-like balance law associated with the rate of increase of the area of the cracks and includes the effects of forces maintaining the crack growth and the inertia of microscopic particles surrounding the cracks. The basic developments represent an idealized characterization of inelastic behaviour in the presence of crack growth, which accounts for energy dissipation without explicit use of macroscopic plasticity effects. A physically plausible constraint on the rate of crack growth is adopted to simplify the theory. To ensure that the results of the theory are physically reasonable, the constitutive response of the dependent variables are significantly restricted by consideration both of the energetic effects and of the microscopic processes that give rise to crack growth. These constitutive developments are in conformity with many of the standard results and observations reported in the literature on fracture mechanics. The predictive nature of the theory is illustrated with reference to two simple examples concerning uniform extensive and compressive straining.

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.

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