Iterated g-Fractional Vector Bochner Integral Representation Formulae and Inequalities for Banach Space Valued Functions

2020 ◽  
pp. 201-221
Author(s):  
George A. Anastassiou
Keyword(s):  
Banach Space ◽  
Integral Representation ◽  
Bochner Integral

scholarly journals An integral for a banach valued function

2009 ◽  
Vol 44 (1) ◽  
pp. 105-113
Author(s):  
Giuseppa Riccobono
Keyword(s):  
Banach Space ◽  
Bochner Integral ◽  
Definition Of

Abstract Using partitions of the unity ((PU)-partition), a new definition of an integral is given for a function f : [a, b] → X, where X is a Banach space, and it is proved that this integral is equivalent to the Bochner integral.

scholarly journals On a characterization of compactness and the Abel-Poisson summability of fourier coefficients in Banach spaces

Filomat ◽  
2016 ◽  
Vol 30 (4) ◽  
pp. 1061-1068
Author(s):  
Seda Öztürk
Keyword(s):  
Banach Space ◽  
Topological Group ◽  
Integral Representation ◽  
Unit Circle ◽  
Banach Spaces ◽  
Fourier Coefficients ◽  
Linear Representation ◽  
Complex Banach Space ◽  
Continuous Linear

In this paper, for an isometric strongly continuous linear representation denoted by ? of the topological group of the unit circle in complex Banach space, we study an integral representation for Abel-Poisson mean A?r (x) of the Fourier coefficients family of an element x, and it is proved that this family is Abel-Poisson summable to x. Finally, we give some tests which are related to characterizations of relatively compactness of a subset by means of Abel-Poisson operator A?r and ?.

scholarly journals Expectation in metric spaces and characterizations of Banach spaces

2009 ◽  
Vol 42 (4) ◽  
Author(s):  
Artur Bator ◽  
Wiesław Zięba
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Metric Space ◽  
Metric Spaces ◽  
Bochner Integral ◽  
Random Elements

AbstractWe consider different definitions of expectation of random elements taking values in metric spaces. All such definitions are valid also in Banach spaces and in this case the results coincide with the Bochner integral. There may exist an isometry between considered metric space and some Banach space and in this case one can use the Bochner integral instead of expectation in metric space. We give some conditions which ensure existence of such isometry, for two different definitions of expectation in metric space.

On Measurability for Vector-Valued Functions

1963 ◽  
Vol 15 ◽  
pp. 613-621 ◽  
Author(s):  
D. O. Snow
Keyword(s):  
Banach Space ◽  
Infinite Series ◽  
Unconditional Convergence ◽  
Integration Theory ◽  
Bochner Integral ◽  
Norm Topology ◽  
Vector Valued Functions ◽  
Vector Valued

The problem of developing an abstract integration theory has been approached from many angles (6). The most general of several definitions based on the norm topology is that of Birkhoff (1), which includes the well-known and widely used Bochner integral (3).The original Birkhoff formulation was based on the notion of unconditional convergence of an infinite series of elements in a Banach space and the closed convex extensions of certain approximating sums.

Integral Representation by Boundary Vector Measures

1982 ◽  
Vol 25 (2) ◽  
pp. 164-168 ◽  
Author(s):  
Paulette Saab
Keyword(s):  
Banach Space ◽  
Integral Representation ◽  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Linear Subspace ◽  
Vector Measure ◽  
Vector Measures ◽  
Boundary Vector

AbstractIn this paper we show that if X is a compact Hausdorff space, A is an arbitrary linear subspace of C(X, C), and if E is a Banach space, then each element L of (A ⊗ E)* can be represented by a boundary E*-valued vector measure of the same norm as L.

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