Nuclear Locally Convex Spaces

Jarchow, Hans

doi:10.1007/978-3-322-90559-8_21

Cited by 113 publications

(202 citation statements)

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“…It is a Montel space since it is barrelled and a projective limit of Montel spaces. The remainder follows from general results ( [18]). …”

Section: Also Reflexive and Weakly Sequentially Complete With The Schmentioning

confidence: 96%

The locally convex topology on the space of meromorphic functions

Grosse‐Erdmann

1995

J Aust Math Soc A

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We give a positive answer to a question of Horst Tietz. A theorem of his that is related to the Mittag-Leffler theorem looks like a duality result under some locally convex topology on the space of meromorphic functions. Tietz has posed the problem of finding such a topology. It is shown that a topology introduced by Holdgriin in 1973 solves the problem. The main tool in the study of this topology is a projective description of it that is derived here. We also argue that Holdgriin's topology is the natural locally convex topology on the space of meromorphic functions.1991 Mathematics subject classification (Amer. Math. Soc): primary 30D30, 46E10; secondary 12J99, 46E25. A problem of TietzLet Q be adomain in C. One natural way of endowing the space M(Q) of meromorphic functions in £2 with a topology is the following. One regards M (£2) as a subspace of the space C(£2, C) of all continuous functions on Q with values in the extended complex plane C, where C carries the chordal metric and C(Q, C) is endowed with the topology of locally uniform convergence. With the inherited topology, r chO r say, M(Q) becomes a metric space; and it is complete if we add the function / ( z ) = oo (cf. [13, VII.3]

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“…It is a Montel space since it is barrelled and a projective limit of Montel spaces. The remainder follows from general results ( [18]). …”

Section: Also Reflexive and Weakly Sequentially Complete With The Schmentioning

confidence: 96%

The locally convex topology on the space of meromorphic functions

Grosse‐Erdmann

1995

J Aust Math Soc A

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“…We use standard locally convex notations and theory as presented in Meise and Vogt [9], Jarchow [5], Bonet, Pérez Carreras [12] and Floret, Wloka [3]. To simplify the notation, let us denote by LCS the category of locally convex topological vector spaces with linear and continuous maps as morphisms and by HD-LCS the full subcategory of spaces whose topology is Hausdorff.…”

Section: Applications and Examplesmentioning

confidence: 99%

Maximal exact structures on additive categories

Sieg

Wegner

2011

Math. Nachr.

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“…This paper continues our study of locally convex properties of spaces with a Toeplitz basis; previously we have studied similar problems related to completeness [PSVI] and barrelledness [PSV2]. [3] Locally convex spaces with Toeplitz decompositions 21 space terminology we refer the reader to [Jr,K6,PeB] or [Wil].) The convergence field of a row-finite matrix T in E is the space c T (E) of all sequences (x k ) from E such that the product T(x k ) is a convergent sequence in E. The sequences in c T (E) are said to be T-convergent.…”

Section: Introductionmentioning

confidence: 95%

Locally Convex Spaces with Toeplitz Decompositions

Paúl¹,

Sáez²,

Virués³

2000

J Aust Math Soc A

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A Toeplitz decomposition of a locally convex space E into subspaces (E k ) with continuous projections (/\) is a decomposition of every x e E as x = J2k Pk x where ordinary summability has been replaced by summability with respect to an infinite and row-finite matrix. We extend to the setting of Toeplitz decompositions a number of results about the locally convex structure of a space with a Schauder decomposition. Namely, we give some necessary or sufficient conditions for being reflexive, a Montel space or a Schwartz space. Roughly speaking, each of these locally convex properties is linked to a property of the convergence of the decomposition. We apply these results to study some structural questions in projective tensor products and spaces with Cesaro bases.1991 Mathematics subject classification (Amer. Math. Soc): primary 46A11,46A25,46A35, 46A45.

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Nuclear Locally Convex Spaces

Cited by 113 publications

References 0 publications

The locally convex topology on the space of meromorphic functions

The locally convex topology on the space of meromorphic functions

Maximal exact structures on additive categories

Locally Convex Spaces with Toeplitz Decompositions

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