Integration of almost periodic functions with values in a Banach space

A well-known result of Ferri and Galindo asserts that the topological group c 0 is not reflexively representable and the algebra WAP ( c 0 ) of weakly almost periodic functions does not separate points and closed subsets. However, it is unknown if the same remains true for a larger important algebra Tame ( c 0 ) of tame functions. Respectively, it is an open question if c 0 is representable on a Rosenthal Banach space. In the present work we show that Tame ( c 0 ) is small in a sense that the unit sphere S and 2 S cannot be separated by a tame function f ∈ Tame ( c 0 ) . As an application we show that the Gromov’s compactification of c 0 is not a semigroup compactification. We discuss some questions.

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Compact operators on a Banach space into the space of almost periodic functions

Proceedings of the Indian Academy of Sciences - Section A ◽

10.1007/bf02881111 ◽

1990 ◽

Vol 100 (1) ◽

pp. 25-36 ◽

Cited By ~ 2

Author(s):

M V Deshpande ◽

M N Parekh

Keyword(s):

Banach Space ◽

Compact Operators ◽

Almost Periodic Functions ◽

Almost Periodic ◽

Periodic Functions

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On some classes of almost periodic functions in abstract spaces

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s016117120440653x ◽

2004 ◽

Vol 2004 (61) ◽

pp. 3237-3247 ◽

Cited By ~ 15

Author(s):

Dariusz Bugajewski ◽

Gaston M. N'Guérékata

Keyword(s):

Banach Space ◽

Partial Differential Equations ◽

Differential Equations ◽

Almost Periodic Functions ◽

Almost Periodic ◽

Superposition Operator ◽

Periodic Functions ◽

Partial Differential ◽

Abstract Spaces

We deal withC(n)-almost periodic functions taking values in a Banach space. We give several properties of such functions, in particular, we investigate their behavior in view of differentiation as well as integration. The superposition operator acting in the space of such functions is also under consideration. Some applications to ordinary as well as partial differential equations are presented. Moreover, we introduce the class of the so-called asymptoticallyC(n)-almost periodic functions and give some of their properties.

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A Remark on Integration of Almost-Periodic Functions

Canadian Mathematical Bulletin ◽

10.4153/cmb-1970-050-3 ◽

1970 ◽

Vol 13 (2) ◽

pp. 249-251

Author(s):

S. Zaidman

Keyword(s):

Banach Space ◽

Banach Spaces ◽

Almost Periodic Functions ◽

Almost Periodic ◽

Periodic Functions

A result proved by Favard for scalar-valued almost-periodic functions has an immediate extension to Banach space valued functions (see [2] and [3] for explicit details).The result says that integrals of almost-periodic functions whose 'spectrum' is at positive distance from 0 are again almost-periodic. Our aim here is to indicate a more general formulation of this result using strongly almost-periodic oneparameter groups of operators in Banach spaces.

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