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Displaying similar documents to “Tauberian operators in p -adic analysis.”

Properties and applications of Tauberian operators.

Manuel González (1990)

Extracta Mathematicae

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Tauberian operators, which appeared in response to a problem in summability [GaW, KW] have found application in several situations: factorization of operators [DFJP], preservation of isomorphic properties of Banach spaces [N, NR], equivalence between the Radon-Nikodym property and the Krein-Milman property [Sch], and generalized Fredholm operators [Ta, Y]. This paper is a survey of the main properties and applications of Tauberian operators.

Quotients of L by reflexive subspaces.

Manuel González, Antonio Martínez-Abejón (1997)

Extracta Mathematicae

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Here we present and example and some results suggesting that there is no infinite-dimensional reflexive subspace Z of L1 ≡ L1[0,1] such that the quotient L1/Z is isomorphic to a subspace of L1.

Tauberian operators on L 1 ( μ ) spaces

Manuel González, Antonio Martínez-Abejón (1997)

Studia Mathematica

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We characterize tauberian operators T : L 1 ( μ ) → Y in terms of the images of disjoint sequences and in terms of the image of the dyadic tree in L 1 [ 0 , 1 ] . As applications, we show that the class of tauberian operators is stable under small norm perturbations and that its perturbation class coincides with the class of all weakly precompact operators. Moreover, we prove that the second conjugate of a tauberian operator T : L 1 ( μ ) → Y is also tauberian, and the induced operator T ̃ : L 1 ( μ ) * * / L 1 ( μ ) → Y * * / Y is an isomorphism into. Also, we show that...

Rosenthal and semi-Tauberian linear relations in normed spaces

Teresa Álvarez, Antonio Martínez-Abejón (2005)

Bollettino dell'Unione Matematica Italiana

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The class of Rosenthal linear relations in normed spaces is introduced and studied in terms of their first and second conjugates. We investigate the relationship between a Rosenthal linear relation and its conjugate. In this paper, we also study the semi-Tauberian linear relations following the pattern followed for the study of the Tauberian linear relations. We prove that the semi-Tauberian linear relations share some of the properties of Tauberian linear relations and they are related...

Supertauberian operators and perturbations.

M. González, A. Martínez-Abejón (1993)

Extracta Mathematicae

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Upper semi-Fredholm operators and tauberian operators in Banach spaces admit the following perturbative characterizations [6], [2]: An operator T: X --> Y is upper semi-Fredholm (tauberian) if and only if for every compact operator K: X --> Y the kernel N(T+K) is finite dimensional (reflexive). In [7] Tacon introduces an intermediate class between upper semi-Fredholm operators and tauberian operators, the supertauberian operators, and he studies this class using non-standard...