Orthogonal sequences in non-archmedean locally convex spaces

Kimpe, N. De Grande-De; Ka̧kol, Jerzy; Pérez-García, C.; Schikhof, W.H.

doi:10.1016/s0019-3577(00)89076-x

Cited by 20 publications

(5 citation statements)

References 3 publications

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“…Every Schauder basis in a Fréchet space F is orthogonal with respect to some (non-decreasing) base (p k ) in P(F ) ( [4], Proposition 1.7).…”

Section: Preliminariesmentioning

confidence: 99%

Fréchet spaces of non-archimedean valued continuous functions

Śliwa

2012

Journal of Mathematical Analysis and Applications

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Let X be an ultraregular space and let K be a complete non-archimedean non-trivially valued field. Assume that the locally convex space E = C c (X; K) of all continuous functions from X to K with the topology τ c of uniform convergence on compact subsets of X is a Fréchet space. We shall prove that E has an orthogonal basis consisting of K-valued characteristic functions of clopen (i.e. closed and open) subsets of X and that it is isomorphic to the product of a countable family of Banach spaces with an orthonormal basis.

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“…Every Schauder basis in a Fréchet space F is orthogonal with respect to some (non-decreasing) base (p k ) in P(F ) ( [4], Proposition 1.7).…”

Section: Preliminariesmentioning

confidence: 99%

Fréchet spaces of non-archimedean valued continuous functions

Śliwa

2012

Journal of Mathematical Analysis and Applications

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“…A Fréchet space is a metrizable complete lcs. Any infinite-dimensional Fréchet space of finite type is isomorphic to the Fréchet space K N of all sequences in K with the topology of pointwise convergence (see [2,Theorem 3.5]).…”

Section: Preliminariesmentioning

confidence: 99%

On Quotients of Non-Archimedean Köthe Spaces

Śliwa¹

2007

Can. math. bull.

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“…By [15, Proposition 9], we have a similar fact for c 0 × K N . For c N 0 it is not true, since there exist Fréchet spaces of countable type without a Schauder basis [14,Theorem 3] and every Fréchet space of countable type is isomorphic to a closed subspace of c N 0 [4,Remark 3.6]. In fact, every infinite-dimensional Fréchet space which is not isomorphic to any of the following spaces (c 0 , K N , c 0 × K N ) contains a closed subspace without a Schauder basis [15,Theorem 7].…”

Section: Introductionmentioning

confidence: 99%

On Complemented Subspaces of Non-Archimedean Power Series Spaces

Śliwa¹,

Ziemkowska²

2011

Can. j. math.

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Abstract. The non-archimedean power series spaces, A 1 (a) and A∞ (b), are the best known and most important examples of non-archimedean nuclear Fréchet spaces. We prove that the range of every continuous linear map from Ap(a) to Aq(b) has a Schauder basis if either p = 1 or p = ∞ and the set M b,a of all bounded limit points of the double sequence (b i /a j ) i, j∈N is bounded. It follows that every complemented subspace of a power series space Ap(a) has a Schauder basis if either p = 1 or p = ∞ and the set Ma,a is bounded.

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Orthogonal sequences in non-archmedean locally convex spaces

Cited by 20 publications

References 3 publications

Fréchet spaces of non-archimedean valued continuous functions

Fréchet spaces of non-archimedean valued continuous functions

On Quotients of Non-Archimedean Köthe Spaces

On Complemented Subspaces of Non-Archimedean Power Series Spaces

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