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Operators on spaces of analytic functions

K. Seddighi (1994)

Studia Mathematica

Let M z be the operator of multiplication by z on a Banach space of functions analytic on a plane domain G. We say that M z is polynomially bounded if ∥ M p ∥ ≤ C ∥ p ∥ G for every polynomial p. We give necessary and sufficient conditions for M z to be polynomially bounded. We also characterize the finite-codimensional invariant subspaces and derive some spectral properties of the multiplication operator in case the underlying space is Hilbert.

Operators with an ergodic power

Teresa Bermúdez, Manuel González, Mostafa Mbekhta (2000)

Studia Mathematica

We prove that if some power of an operator is ergodic, then the operator itself is ergodic. The converse is not true.

Operators with hypercyclic Cesaro means

Fernando León-Saavedra (2002)

Studia Mathematica

An operator T on a Banach space ℬ is said to be hypercyclic if there exists a vector x such that the orbit T ⁿ x n ≥ 1 is dense in ℬ. Hypercyclicity is a strong kind of cyclicity which requires that the linear span of the orbit is dense in ℬ. If the arithmetic means of the orbit of x are dense in ℬ then the operator T is said to be Cesàro-hypercyclic. Apparently Cesàro-hypercyclicity is a strong version of hypercyclicity. We prove that an operator is Cesàro-hypercyclic if and only if there exists a vector...

Operator-valued n-harmonic measure in the polydisc

Anders Olofsson (2004)

Studia Mathematica

An operator-valued multi-variable Poisson type integral is studied. In Section 2 we obtain a new equivalent condition for the existence of a so-called regular unitary dilation of an n-tuple T=(T₁,...,Tₙ) of commuting contractions. Our development in Section 2 also contains a new proof of the classical dilation result of S. Brehmer, B. Sz.-Nagy and I. Halperin. In Section 3 we turn to the boundary behavior of this operator-valued Poisson integral. The results obtained in this section improve upon...

Optimal nonlinear transformations of random variables

Aldo Goia, Ernesto Salinelli (2010)

Annales de l'I.H.P. Probabilités et statistiques

In this paper we deepen the study of the nonlinear principal components introduced by Salinelli in 1998, referring to a real random variable. New insights on their probabilistic and statistical meaning are given with some properties. An estimation procedure based on spline functions, adapting to a statistical framework the classical Rayleigh–Ritz method, is introduced. Asymptotic properties of the estimator are proved, providing an upper bound for the rate of convergence under suitable mild conditions....

Orbits of linear operators and Banach space geometry

Jean-Matthieu Augé (2012)

Studia Mathematica

Let T be a bounded linear operator on a (real or complex) Banach space X. If (aₙ) is a sequence of non-negative numbers tending to 0, then the set of x ∈ X such that ||Tⁿx|| ≥ aₙ||Tⁿ|| for infinitely many n’s has a complement which is both σ-porous and Haar-null. We also compute (for some classical Banach space) optimal exponents q > 0 such that for every non-nilpotent operator T, there exists x ∈ X such that ( | | T ⁿ x | | / | | T ⁿ | | ) ∉ ℓ q ( ℕ ) , using techniques which involve the modulus of asymptotic uniform smoothness of X.

Orbits under a class of isometries of L¹[0,1]

Terje Hõim (2004)

Studia Mathematica

We study the orbits of isometries of L¹[0,1]. For a certain class of isometries we show that the set of functions f in L¹[0,1] for which the orbit of f under the isometry T is equivalent to the usual canonical basis e₁,e₂,e₃,... of l¹ is an open dense set. In the proof we develop a new method to get copies of l¹ inside L¹[0,1] using geometric progressions. This method does not use disjoint or relatively disjoint supports, which seems to be the most common way to get such copies. We also use this...

Order bounded orthosymmetric bilinear operator

Elmiloud Chil (2011)

Czechoslovak Mathematical Journal

It is proved by an order theoretical and purely algebraic method that any order bounded orthosymmetric bilinear operator b : E × E → F where E and F are Archimedean vector lattices is symmetric. This leads to a new and short proof of the commutativity of Archimedean almost f -algebras.

Currently displaying 481 – 500 of 503