Descriptive Topology and Functional Analysis: In Honour of by Juan Carlos Ferrando, Manuel López-Pellicer

By Juan Carlos Ferrando, Manuel López-Pellicer

Descriptive topology and practical research, with wide fabric demonstrating new connections among them, are the topic of the 1st element of this paintings. purposes to areas of constant features, topological Abelian teams, linear topological equivalence and to the separable quotient challenge are incorporated and are awarded as open difficulties. the second one part is dedicated to Banach areas, Banach algebras and operator idea. every one bankruptcy offers loads of important and demanding contemporary theorems with an summary discussing the cloth within the bankruptcy. every one bankruptcy can nearly be obvious as a survey masking a selected sector.

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Additional resources for Descriptive Topology and Functional Analysis: In Honour of Jerzy Kakol’s 60th Birthday (Springer Proceedings in Mathematics & Statistics)

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1 Introduction z The Riemann zeta function defined on ≡z > 1 as Γ (z) := → k=1 1/k and extended by analytic continuation to the whole complex plane, except in z = 1, where it has a simple pole, has associated a strip, (0, 1) × R, called critical strip which contains the non-trivial zeros of Γ (z). It is well known that in 1859, B. Riemann, formulated his famous conjecture on the location of the zeros of Γ (z) under the form “it is very likely that the complex zeros of Γ (z) all have real part equal to 1/2”.

On S-barrelled spaces. Results Math. : The Mackey-Arens and Hahn-Banach theorems for spaces over valued fields. In: Proceedings of the 3rd International Conference on p-adic Functional Analysis (Aubière 1994). Ann. Math. : The Mackey-Arens property for spaces over valued fields. Bull. Polish Acad. Sci. Math. : Mode of increase of power similar sets of polynomials. Bull. Fac. Sci. Assiut Univ. : A strong barrelledness property for spaces C(X, E). Note Mat. : CS-barrelled spaces. Collect. Math.

Consequently, there is a zero of Γn (z) in the half-plane ≡z > 1 . In 1968 Spira [32, 33] demonstrated that the same happens for n = 19, that is, he proved that Γ19 (z) has a zero in the half-plane ≡z > 1. Levinson [19, Theorem 1] in 1973 found an asymptotic formula, for large n, for the location of the zeros of Γn (z) near the point z = 1. In particular, he proved that those zeros have real part less than 1. Voronin [38] in 1974 showed that Γn (z) has zeros in ≡z > 1, for infinitely many n. A sharp result on the upper bound bΓn (z) := sup {≡z : Γn (z) = 0} was given in 2001 by Montgomery and Vaughan in [21].

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