A simple example of a universal Schwartz space

Randtke, Daniel J.

doi:10.1090/s0002-9939-1973-0312192-7

Cited by 12 publications

(5 citation statements)

References 10 publications

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“…If p = oo, one obtains in the same manner that E is the inductive limit of isomorphic copies of the universal Schwartz space Ira, z(m, 10] of [6] and [19].…”

Section: Be Given An Lcs E Is a (P Q)i-space [ A (P Q)h-space / Ifmentioning

confidence: 81%

Factorization through inclusion mappings betweenl p-spaces

Jarchow

1976

Math. Ann.

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“…If p = oo, one obtains in the same manner that E is the inductive limit of isomorphic copies of the universal Schwartz space Ira, z(m, 10] of [6] and [19].…”

Section: Be Given An Lcs E Is a (P Q)i-space [ A (P Q)h-space / Ifmentioning

confidence: 81%

Factorization through inclusion mappings betweenl p-spaces

Jarchow

1976

Math. Ann.

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“…The above corollary, therefore, yields a simpler and a more general approach to the construction of universal generators for Schwartz spaces. The results of Randtke [8] and Jarchow [3] on these constructions, therefore, follow as special cases of this more general approach.…”

Section: Corollariesmentioning

confidence: 86%

A note on embedding into product spaces

Sofi

2006

Czech Math J

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“…The sets U α (with α ∈ c 0 ) constitute a neighbourhood basis at 0 of S(c 0 ), see [23]. To see why S(c 0 ) is not unitarily representable we need a couple of results on the structure of linear operators with values in L 0 .…”

Section: On the Limits Of The Class Of Unitarily Representable Groupsmentioning

confidence: 99%

On unitary representability of topological groups

Galindo

2008

Math. Z.

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Abstract. We prove that the additive group (E * , τ k (E)) of an L∞-Banach space E, with the topology τ k (E) of uniform convergence on compact subsets of E, is topologically isomorphic to a subgroup of the unitary group of some Hilbert space (is unitarily representable). This is the same as proving that the topological group (E * , τ k (E)) is uniformly homeomorphic to a subset of ℓ κ 2 for some κ. As an immediate consequence, preduals of commutative von Neumann algebras or duals of commutative C * -algebras are unitarily representable in the topology of uniform convergence on compact subsets. The unitary representability of free locally convex spaces (and thus of free Abelian topological groups) on compact spaces, follows as well.The above facts cannot be extended to noncommutative von Neumann algebras or general Schwartz spaces.

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A simple example of a universal Schwartz space

Abstract: A Schwartz space E is universal if every Schwartz space is topologically isomorphic to a linear subspace of some power E' of E. In this paper concrete examples of universal Schwartz spaces are exhibited.

Cited by 12 publications

References 10 publications

Factorization through inclusion mappings betweenl p-spaces

Factorization through inclusion mappings betweenl p-spaces

A note on embedding into product spaces

On unitary representability of topological groups

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