[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 ...
[EN] By the von Neumann inequality for homogeneous polynomials there exists a positive constant C-k,C-q(n) such that for every k-homogeneous polynomial p in n variables and every n-tuple of commuting operators (T-1, ..., ...
[EN] The Bohr–Bohnenblust–Hille theorem states that the width of the strip in the complex plane on which an
ordinary Dirichlet series P
n
ann
−s
converges uniformly but not absolutely is less than or equal to 1
2
, ...
[EN] The Cluster Value Theorem is known for being a weak version of the classical Corona Theorem. Given a Banach space X, we study the Cluster Value Problem for the ball algebra A(u)(B-X), the Banach algebra of all uniformly ...
[EN] Recent results on Dirichlet series Sigma(n) a(n) 1/n(s), s is an element of C, with coefficients a(n) in an infinite dimensional Banach space X show that the maximal width of uniform but not absolute convergence ...
Defant, Andreas; Sevilla Peris, Pablo(Oxford University Press (OUP), 2012-09)
[EN] If E is a Banach sequence space, then each holomorphic function defines a formal power series ¿ ¿ c ¿(f) z ¿. The problem of when such an expansion converges absolutely and actually represents the function goes back ...
[EN] While the article was in publication process, we found a mistake in a key tool for the proof one of the main results. As a consequence, our result on the ball A(u)(B-X) algebra remains open. For the algebra H-b(X) we ...
[EN] We study extendibility of diagonal multilinear operators from l(p) to l(p) spaces. We determine the values of and for which every diagonal -linear operator is extendible, and those for which the only extendible ones ...
[EN] A classical result of Harald Bohr linked the study of convergent and bounded Dirichlet series on the right half plane with bounded holomorphic functions on the open unit ball of the space c(0) f complex null sequences. ...
[EN] We estimate the -norm of finite Dirichlet polynomials with coefficients in a Banach space. Our estimates quantify several recent results on Bohr's strips of uniform but non absolute convergence of Dirichlet series in ...
DANIEL CARANDO; Sevilla Peris, Pablo(Springer Verlag (Germany), 2014-03)
[EN] We study Hahn-Banach extensions of multilinear forms defined on Banach sequence spaces. We characterize c(0) in terms of extension of bilinear forms, and describe the Banach sequence spaces in which every bilinear ...
Conejero, J. Alberto; Seoane-Sepulveda, Juan B.; Sevilla Peris, Pablo(John Wiley & Sons, 2017)
[EN] We employ a classical result by Toeplitz (1913) and the seminal work by Bohnenblust and Hille on Dirichlet series (1931) to show that the set of continuous m-homogeneous non-analytic polynomials on c(o) contains an ...
[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 ...
[EN] We introduce non-linear versions of the classical cotype of Banach spaces. We show that spaces with l.u.st. and cotype, and spaces having Fourier cotype enjoy our non-linear cotype. We apply these concepts to get ...
Dimant, Verónica; Sevilla Peris, Pablo(Universitat Autonoma de Barcelona, 2016)
[EN] We investigate the summability of the coefficients of m-homogeneous polynomials and m-linear mappings defined on l(p) spaces. In our research we obtain results on the summability of the coefficients of m-linear mappings ...
Defant, Andreas; Sevilla Peris, Pablo(Adam Mickiewicz University The Faculty of Mathematics and Computer Science, 2014)
[EN] In 1931 H.F.Bohnenblust and E.Hille published a very important paper in which
not only did they solve a long standing problem on convergence of Dirichlet series, but also
gave a general version of a celebrated ...
We give a variant of the Bohenblust-Hille inequality which, for certain families of polynomials, leads to constants with polynomial growth in the degree.
Defant, Andreas; Sevilla Peris, Pablo(Institute of Mathematics, Polish Academy of Sciences, 2016)
[EN] Let x(m, n) be the unconditional basis constant of the monomial basis Z alpha, alpha is an element of N(0)n with vertical bar alpha vertical bar = m, of the Banach space of all m-homogeneous polynomials inn complex ...