Displaying similar documents to “On certain barrelled normed spaces”

Some characterizations of ultrabornological spaces

Manuel Valdivia (1974)

Annales de l'institut Fourier

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Let U be an infinite-dimensional separable Fréchet space with a topology defined by a family of norms. Let F be an infinite-dimensional Banach space. Then F is the inductive limit of a family of spaces equal to E . The choice of suitable classes of Fréchet spaces allows to give characterizations of ultrabornological spaces using the result above.. Let Ω be a non-empty open set in the euclidean n -dimensional space R n . Then F is the inductive limit of a family of spaces equal to D ( Ω ) . ...

On the closure of spaces of sums of ridge functions and the range of the X -ray transform

Jan Boman (1984)

Annales de l'institut Fourier

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For a R n { 0 } and Ω an open bounded subset of R n definie L p ( Ω , a ) as the closed subset of L p ( Ω ) consisting of all functions that are constant almost everywhere on almost all lines parallel to a . For a given set of directions a ν R n { 0 } , ν = 1 , ... , m , we study for which Ω it is true that the vector space ( * ) L p ( Ω , a 1 ) + + L p ( Ω , a m ) is a closed subspace of L p ( Ω ) . This problem arizes naturally in the study of image reconstruction from projections (tomography). An essentially equivalent problem is to decide whether a certain matrix-valued differential operator...

On B r -completeness

Manuel Valdivia (1975)

Annales de l'institut Fourier

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In this paper it is proved that if { E n } n = 1 and { F n } n = 1 are two sequences of infinite-dimensional Banach spaces then H = n = 1 E n × n = 1 F n is not B r -complete. If { E n } n = 1 and { F n } n = 1 are also reflexive spaces there is on H a separated locally convex topology , coarser than the initial one, such that H [ ] is a bornological barrelled space which is not an inductive limit of Baire spaces. It is given also another results on B r -completeness and bornological spaces.

An almost-sure estimate for the mean of generalized Q -multiplicative functions of modulus 1

Jean-Loup Mauclaire (2000)

Journal de théorie des nombres de Bordeaux

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Let Q = ( Q k ) k 0 , Q 0 = 1 , Q k + 1 = q k Q k , q k 2 , be a Cantor scale, 𝐙 Q the compact projective limit group of the groups 𝐙 / Q k 𝐙 , identified to 0 j k - 1 𝐙 / q j 𝐙 , and let μ be its normalized Haar measure. To an element x = { a 0 , a 1 , a 2 , } , 0 a k q k + 1 - 1 , of 𝐙 Q we associate the sequence of integral valued random variables x k = 0 j k a j Q j . The main result of this article is that, given a complex 𝐐 -multiplicative function g of modulus 1 , we have lim x k x ( 1 x k n x k - 1 g ( n ) - 0 j k 1 q j 0 a q j g ( a Q j ) ) = 0 μ -a.e .

Mapping Properties of c 0

Paul Lewis (1999)

Colloquium Mathematicae

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Bessaga and Pełczyński showed that if c 0 embeds in the dual X * of a Banach space X, then 1 embeds as a complemented subspace of X. Pełczyński proved that every infinite-dimensional closed linear subspace of 1 contains a copy of 1 that is complemented in 1 . Later, Kadec and Pełczyński proved that every non-reflexive closed linear subspace of L 1 [ 0 , 1 ] contains a copy of 1 that is complemented in L 1 [ 0 , 1 ] . In this note a traditional sliding hump argument is used to establish a simple mapping property of...

Partial differential operators depending analytically on a parameter

Frank Mantlik (1991)

Annales de l'institut Fourier

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Let P ( λ , D ) = | α | m a α ( λ ) D α be a differential operator with constant coefficients a α depending analytically on a parameter λ . Assume that the family { P( λ ,D) } is of constant strength. We investigate the equation P ( λ , D ) 𝔣 λ g λ where 𝔤 λ is a given analytic function of λ with values in some space of distributions and the solution 𝔣 λ is required to depend analytically on λ , too. As a special case we obtain a regular fundamental solution of P( λ ,D) which depends analytically on λ . This result answers a question of L. Hörmander. ...