Certain General Questions of the Theory of Probability Measures in Linear Spaces

Mushtari, D. Kh.

doi:10.1137/1118005

Cited by 14 publications

(4 citation statements)

References 6 publications

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“…(iv) The necessity part of Bochners theorem in the setting of lcs was proved by Minlos [17] who showed its validity in metrisable nuclear spaces. The converse that the validity of Bochners theorem in a metrisable lcs X implies nuclearity of X is a deep result of D. Muschtari [18].…”

Section: Definitions and Examplesmentioning

confidence: 95%

Around finite-dimensionality in functional analysis: a personal perspective

Sofi

2012

RACSAM

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1: As objects of study in functional analysis, Hilbert spaces stand out as special objects of study as do nuclear spaces (ala Grothendieck) in view of a rich geometrical structure they possess as Banach and Frechet spaces, respectively. On the other hand, there is the class of Banach spaces including certain function spaces and sequence spaces which are distinguished by a poor geometrical structure and are subsumed under the class of so-called Hilbert-Schmidt spaces. It turns out that these three classes of spaces are mutually disjoint in the sense that they intersect precisely in finite dimensional spaces. However, it is remarkable that despite this mutually exclusive character, there is an underlying commonality of approach to these disparate classes of objects in that they crop up in certain situations involving a single phenomenon-the phenomenon of finite dimensionality-which, by definition, is a generic term for those properties of Banach spaces which hold good in finite dimensional spaces but fail in infinite dimension.

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Section: Definitions and Examplesmentioning

confidence: 95%

Around finite-dimensionality in functional analysis: a personal perspective

Sofi

2012

RACSAM

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“…The characterization of those real separable Banach spaces which are S-spaces was given by Muschtari (cf. [9,10], see also [1] and [3]). …”

Section: V*~(v V*)~--~(v V*)~f and Bymentioning

confidence: 98%

On Sazonov type topology inp-adic Banach space

Madrecki

1985

Math Z

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“…(1) If E is a a-Hilbert space or a Frechet space, then the answer is affirmative (see Badrikian [2], Gelfand and Vilenkin [4], Minlos, [11], Mushtari [12], Umemura [20] and Yamasaki [21]). …”

Section: §1 Introductionmentioning

confidence: 99%

“…(2) If E is barrelled and if E is a projective limit of L°-embeddable Banach spaces, then the answer is affirmative (see Millington [10], Mushtari [12], Okazaki and Takahashi [14]). …”

Section: §1 Introductionmentioning

confidence: 99%

The Converse of Minlos' Theorem

Okazaki¹,

Takahashi²

1994

Publ. Res. Inst. Math. Sci.

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Let ^ be the class of barrelled locally convex Hausdorff space E such that E'^ satisfies the property B in the sense of Pietsch. It is shown that if Ee^and if each continuous cylinder set measure on E' is <7(£', E) -Radon, then E is nuclear. There exists an example of non-nuclear Frechet space E such that each continuous Gaussian cylinder set measure on £'is 0(E', E)-Radon. Let q be 2 < q < oo. Suppose that E e ^ and £ is a projective limit of Banach space {E a } such that the dual E' a is of cotype q for every ct,. Suppose also that each continuous Gaussian cylinder set measure on E' is a(E',E) -Radon. Then E is nuclear. §1. Introduction Let £ be a nuclear locally convex Hausdorff space, then each continuous cylinder set measure on E' is

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Certain General Questions of the Theory of Probability Measures in Linear Spaces

Cited by 14 publications

References 6 publications

Around finite-dimensionality in functional analysis: a personal perspective

Around finite-dimensionality in functional analysis: a personal perspective

On Sazonov type topology inp-adic Banach space

The Converse of Minlos' Theorem

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