Spaces of Vector-Valued Continuous Functions

Schmets, Jean

doi:10.1007/bfb0061450

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Js-t/21

Remark 221

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1985

2023

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Cited by 34 publications

(2 citation statements)

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“…We denote by 38 G the a-algebra of Borel subsets of G. We recall some results on integration of functions f : G -*• X with respect to X'-valued measures on 3S G , denoted by M(G, X'). For details one may refer Schmets [34]. Let /x € M(G, X') and for every x, let \i x denote the scalar measure on 38 G defined by fi x (E) :-(x, /x(£)) for every E e 38 G .…”

Section: Js-t/2mentioning

confidence: 99%

Vector valued mean-periodic functions on groups

Devaraj¹,

Rana²

2002

J. Aust. Math. Soc.

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Section: Js-t/2mentioning

confidence: 99%

Vector valued mean-periodic functions on groups

Devaraj¹,

Rana²

2002

J. Aust. Math. Soc.

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“…A survey of what is known about spaces of real valued or real vector space valued continuous functions can be found in [9] and [11]. REMARK 2.3.…”

Section: Remark 22mentioning

confidence: 99%

Duality properties of spaces of non-Archimedean valued functions

Govaerts

1987

J Aust Math Soc A

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Let C(X, F) be the space of all continuous functions from the ultraregular compact Hausdorff space X into the separated locally Jf-convex space F; AT is a complete, but not necessarily spherically complete, non-Archimedean valued field and C(X, F) is provided with the topology of uniform convergence on X. We prove that C( X, F) is ^-barrelled (respectively AT-quasibarrelled) if and only if F is AT-barrelled (respectively /f-quasibarrelled). This is not true in the case of R or C-valued functions. No complete characterization of the if-bornological spaces C( X, F) is obtained, but our results are, nevertheless, slightly better than the Archimedean ones. Finally, we introduce a notion of A"-ultrabornological spaces for K non-spherically complete and use it to study Af-ultrabornological spaces C(X, F).1980 Mathematics subject classification (Amer. Math. Soc.): 46 P 05.

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Null Sequences in Coechelon Spaces

Dierolf

Domański

1997

Mathematische Nachrichten

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We prove that for any Kothe matrices a and b if T : Ai(a) --+ Ao(b) maps bounded sets into relatively compact sets, then T factorizes through a Frbchet Montel space. This is a consequence of a given description of those compact subsets in a coechelon space k,(v) of type 00 which are contained in an absolutely convex hull of a null sequence. An example of a compact set which is not of that form is given. 1991 Mathematics Subject Classification. Primary 46 A 45, 46 A50, 47 B 07.

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Spaces of Vector-Valued Continuous Functions

Cited by 34 publications

References 5 publications

Vector valued mean-periodic functions on groups

Vector valued mean-periodic functions on groups

Duality properties of spaces of non-Archimedean valued functions

Null Sequences in Coechelon Spaces

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