A hypercyclic finite rank perturbation of a unitary operator

A unitary operator $V$ and a rank $2$ operator $R$ acting on a Hilbert space \H are constructed such that $V+R$ is hypercyclic. This answers affirmatively a question of Salas whether a finite rank perturbation of a hyponormal operator can be supercyclic.Comment: published in Mathematische Annale

On a conjecture regarding the upper graph box dimension of bounded subsets of the real line

Let X \subset R be a bounded set; we introduce a formula that calculates the upper graph box dimension of X (i.e.the supremum of the upper box dimension of the graph over all uniformly continuous functions defined on X). We demonstrate the strength of the formula by calculating the upper graph box dimension for some sets and by giving an "one line" proof, alternative to the one given in [1], of the fact that if X has finitely many isolated points then its upper graph box dimension is equal to the upper box dimension plus one. Furthermore we construct a collection of sets X with infinitely many isolated points, having upper box dimension a taking values from zero to one while their graph box dimension takes any value in [max{2a,1},a + 1], answering this way, negatively to a conjecture posed in [1]

Portugal and Angola: the politics of a troubled media relationship

In his last text of 2016, published on Christmas day, the editor of Angola’s official newspaper, Jornal de Angola, wrote a ‘message of harmony’ where he chose to focus on diplomatic relations with the former colonial power. José Ribeiro’s reading was clear: “Forty one years after independence the Portuguese elites still treat us impolitely as if we were their slaves” (Ribeiro, 2016). This posture would be reinforced precisely a week later in the first editorial of 2017: “Angola will not cease to be an independent country (…) no longer willing to accept mouldy neo-colonial impositions from abroad” (Ribeiro, 2017).(undefined)info:eu-repo/semantics/publishedVersio

Almost sure-sign convergence of Hardy-type Dirichlet series

[EN] Hartman proved in 1939 that the width of the largest possible strip in the complex plane on which a Dirichlet series is uniformly a.s.- sign convergent (i.e., converges uniformly for almost all sequences of signs epsilon (n) = +/- 1) but does not convergent absolutely, equals 1/2. We study this result from a more modern point of view within the framework of so-called Hardytype Dirichlet series with values in a Banach space.Supported by CONICET-PIP 11220130100329CO, PICT 2015-2299 and UBACyT 20020130100474BA. Supported by MICINN MTM2017-83262-C2-1-P. Supported by MICINN MTM2017-83262-C2-1-P and UPV-SP20120700.Carando, D.; Defant, A.; Sevilla Peris, P. (2018). Almost sure-sign convergence of Hardy-type Dirichlet series. Journal d Analyse Mathématique. 135(1):225-247. https://doi.org/10.1007/s11854-018-0034-yS2252471351A. Aleman, J.-F. Olsen, and E. Saksman, Fourier multipliers for Hardy spaces of Dirichlet series, Int. Math. Res. Not. IMRN 16 (2014), 4368–4378.R. Balasubramanian, B. Calado, and H. Queffélec, The Bohr inequality for ordinary Dirichlet series Studia Math. 175 (2006), 285–304.F. Bayart, Hardy spaces of Dirichlet series and their composition operators, Monatsh. Math. 136 (2002), 203–236.F. Bayart, A. Defant, L. Frerick, M. Maestre, and P. Sevilla-Peris, Monomial series expansion of Hp-functions and multipliers ofHp-Dirichlet series, Math. Ann. 368 (2017), 837–876.F. Bayart, D. Pellegrino, and J. B. Seoane-Sepúlveda, The Bohr radius of the n-dimensional polydisk is equivalent to $$\sqrt {\left( {\log n} \right)/n}$$ ( log n ) / n , Adv. Math. 264 (2014), 726–746.F. Bayart, H. Queffélec, and K. Seip, Approximation numbers of composition operators on Hp spaces of Dirichlet series, Ann. Inst. Fourier (Grenoble) 66 (2016), 551–588.H. F. Bohnenblust and E. Hille. On the absolute convergence of Dirichlet series, Ann. of Math. (2) 32 (1931), 600–622.H. Bohr, Über die Bedeutung der Potenzreihen unendlich vieler Variablen in der Theorie der Dirichlet–schen Reihen $$\sum {\frac{{{a_n}}}{{{n^s}}}}$$ ∑ a n n s , Nachr. Ges.Wiss. Göttingen, Math. Phys. Kl., 1913, pp. 441–488.D. Carando, A. Defant, and P. Sevilla-Peris, Bohr’s absolute convergence problem for Hp- Dirichlet series in Banach spaces, Anal. PDE 7 (2014), 513–527.D. Carando, A. Defant, and P. Sevilla-Peris, Some polynomial versions of cotype and applications, J. Funct. Anal. 270 (2016), 68–87.B. J. Cole and T. W. Gamelin, Representing measures and Hardy spaces for the infinite polydisk algebra, Proc. London Math. Soc. (3) 53 (1986), 112–142.R. de la Bretèche. Sur l’ordre de grandeur des polynômes de Dirichlet, Acta Arith. 134 (2008), 141–148.A. Defant, L. Frerick, J. Ortega-Cerdà, M. Ounäies, and K. Seip, The Bohnenblust-Hille inequality for homogeneous polynomials is hypercontractive, Ann. of Math. (2) 174 (2011), 485–497.A. Defant, D. García, M. Maestre, and D. Pérez-García, Bohr’s strip for vector valued Dirichlet series, Math. Ann. 342 (2008), 533–555.A. Defant, M. Maestre, and U. Schwarting, Bohr radii of vector valued holomorphic functions, Adv. Math. 231 (2012), 2837–2857.A. Defant and A. Pérez, Hardy spaces of vector-valued Dirichlet series, StudiaMath. (to appear), 2018 DOI: 10.4064/sm170303-26-7.A. Defant, U. Schwarting, and P. Sevilla-Peris, Estimates for vector valued Dirichlet polynomials, Monatsh. Math. 175 (2014), 89–116.J. Diestel, H. Jarchow, and A. Tonge, Absolutely Summing Operators, Cambridge University Press, Cambridge, 1995.P. Hartman, On Dirichlet series involving random coefficients, Amer. J. Math. 61 (1939), 955–964.H. Hedenmalm, P. Lindqvist, and K. Seip, A Hilbert space of Dirichlet series and systems of dilated functions in L2(0, 1), Duke Math. J. 86 (1997), 1–37.A. Hildebrand, and G. Tenenbaum, Integers without large prime factors, J. Thor. Nombres Bordeaux 5 (1993), 411–484.S. V. Konyagin and H. Queffélec, The translation 1/2 in the theory of Dirichlet series, Real Anal. Exchange 27 (2001/02) 155–175.J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces. II, Springer-Verlag, Berlin, 1979.B. Maurizi and H. Queffélec, Some remarks on the algebra of bounded Dirichlet series, J. Fourier Anal. Appl. 16 (2010), 676–692.H. Queffélec, H. Bohr’s vision of ordinary Dirichlet series; old and new results, J. Anal. 3 (1995), 43–60.H. Queffélec and M. Queffélec, Diophantine Approximation and Dirichlet Series, Hindustan Book Agency, New Delhi, 2013.G. Tenenbaum, Introduction to Analytic and Probabilistic Number Theory, Cambridge University Press, Cambridge, 1995

Abstract basins of attraction

Abstract basins appear naturally in different areas of several complex variables. In this survey we want to describe three different topics in which they play an important role, leading to interesting open problems

Nigerian scam e-mails and the charms of capital

So-called '419' or 'advance-fee' e-mail frauds have proved remarkably successful. Global losses to these scams are believed to run to billions of dollars. Although it can be assumed that the promise of personal gain which these e-mails hold out is part of what motivates victims, there is more than greed at issue here. How is it that the seemingly incredible offers given in these unsolicited messages can find an audience willing to treat them as credible? The essay offers a speculative thesis in answer to this question. Firstly, it is argued, these scams are adept at exploiting common presuppositions in British and American culture regarding Africa and the relationships that are assumed to exist between their nations and those in the global south. Secondly, part of the appeal of these e-mails lies in the fact that they appear to reveal the processes by which wealth is created and distributed in the global economy. They thus speak to their readers’ attempts to map or conceptualise the otherwise inscrutable processes of that economy. In the conclusion the essay looks at the contradictions in the official state response to this phenomena

Multipliers of Dirichlet series and monomial series expansions of holomorphic functions in infinitely many variables

[EN] Let H-infinity be the set of all ordinary Dirichlet series D = Sigma(n) a(n)(n-1) ann-s representing bounded holomorphic functions on the right half plane. A completely multiplicative sequence (b(n)) of complex numbers is said to be an l(1)-multiplier for H-infinity whenever Sigma(n vertical bar)a(n)b(n vertical bar) < infinity for every D is an element of H-infinity. We study the problem of describing such sequences (b(n)) in terms of the asymptotic decay of the subsequence (b(pj)), where p(j) denotes the j th prime number. Given a completely multiplicative sequence b = (b(n)) we prove (among other results): b is an l(1)-multiplier for H-infinity provided vertical bar b(pj)vertical bar < 1 for all j and (lim(n)) over bar 1/log(n) Sigma(n)(j=1) b(p j)*(2) < 1, and conversely, if b is an l(1)-multiplier for H-infinity, then vertical bar b(pj)vertical bar < 1 for all j and (lim(n)) over bar 1/log(n) Sigma(n)(j=1) b(p j)*(2) <= 1 (here b* stands for the decreasing rearrangement of b). Following an ingenious idea of Harald Bohr it turns out that this problem is intimately related with the question of characterizing those sequences z in the infinite dimensional polydisk D-infinity (the open unit ball of l(infinity)) for which every bounded and holomorphic function f on D-infinity has an absolutely convergent monomial series expansion Sigma(alpha) partial derivative alpha f (0)/alpha! z alpha. Moreover, we study analogous problems in Hardy spaces of Dirichlet series and Hardy spaces of functions on the infinite dimensional polytorus T-infinity.The second, fourth and fifth authors were supported by MINECO and FEDER Project MTM2014-57838-C2-2-P. The fourth author was also supported by PrometeoII/2013/013. The fifth author was also supported by project SP-UPV20120700.Bayart, F.; Defant, A.; Frerick, L.; Maestre, M.; Sevilla Peris, P. (2017). Multipliers of Dirichlet series and monomial series expansions of holomorphic functions in infinitely many variables. Mathematische Annalen. 368(1-2):837-876. https://doi.org/10.1007/s00208-016-1511-1S8378763681-2Aleman, A., Olsen, J.-F., Saksman, E.: Fatou and brother Riesz theorems in the infinite-dimensional polydisc. arXiv:1512.01509Balasubramanian, R., Calado, B., Queffélec, H.: The Bohr inequality for ordinary Dirichlet series. 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