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Pointwise limits for sequences of orbital integrals

Claire Anantharaman-Delaroche (2010)

Colloquium Mathematicae

In 1967, Ross and Stromberg published a theorem about pointwise limits of orbital integrals for the left action of a locally compact group G on (G,ρ), where ρ is the right Haar measure. We study the same kind of problem, but more generally for left actions of G on any measure space (X,μ), which leave the σ-finite measure μ relatively invariant, in the sense that sμ = Δ(s)μ for every s ∈ G, where Δ is the modular function of G. As a consequence, we also obtain a generalization of a theorem of Civin...

Pointwise multiplication operators on weighted Banach spaces of analytic functions

J. Bonet, P. Domański, M. Lindström (1999)

Studia Mathematica

For a wide class of weights we find the approximative point spectrum and the essential spectrum of the pointwise multiplication operator M φ , M φ ( f ) = φ f , on the weighted Banach spaces of analytic functions on the disc with the sup-norm. Thus we characterize when M φ ' is Fredholm or is an into isomorphism. We also study cyclic phenomena for the adjoint map M φ ' .

Pointwise multipliers on martingale Campanato spaces

Eiichi Nakai, Gaku Sadasue (2014)

Studia Mathematica

We introduce generalized Campanato spaces p , ϕ on a probability space (Ω,ℱ,P), where p ∈ [1,∞) and ϕ: (0,1] → (0,∞). If p = 1 and ϕ ≡ 1, then p , ϕ = B M O . We give a characterization of the set of all pointwise multipliers on p , ϕ .

Poisson's equation and characterizations of reflexivity of Banach spaces

Vladimir P. Fonf, Michael Lin, Przemysław Wojtaszczyk (2011)

Colloquium Mathematicae

Let X be a Banach space with a basis. We prove that X is reflexive if and only if every power-bounded linear operator T satisfies Browder’s equality x ∈ X : s u p n | | ∑ k = 1 n T k x | | < ∞ = (I-T)X . We then deduce that X (with a basis) is reflexive if and only if every strongly continuous bounded semigroup T t : t ≥ 0 with generator A satisfies A X = x ∈ X : s u p s > 0 | | ∫ 0 s T t x d t | | < ∞ . The range (I-T)X (respectively, AX for continuous time) is the space of x ∈ X for which Poisson’s equation (I-T)y = x (Ay = x in continuous time) has a solution y ∈ X; the above equalities for the ranges...

Polar lattices from the point of view of nuclear spaces.

Wojciech Banaszczyk (1989)

Revista Matemática de la Universidad Complutense de Madrid

The aim of this survey article is to show certain questions concerning nuclear spaces and linear operators in normed spaces lead to questions from geometry of numbers.

Polaroid type operators and compact perturbations

Chun Guang Li, Ting Ting Zhou (2014)

Studia Mathematica

A bounded linear operator T acting on a Hilbert space is said to be polaroid if each isolated point in the spectrum is a pole of the resolvent of T. There are several generalizations of the polaroid property. We investigate compact perturbations of polaroid type operators. We prove that, given an operator T and ε > 0, there exists a compact operator K with ||K|| < ε such that T + K is polaroid. Moreover, we characterize those operators for which a certain polaroid type property is stable under...

Polaroid type operators under perturbations

Pietro Aiena, Elvis Aponte (2013)

Studia Mathematica

A bounded operator T defined on a Banach space is said to be polaroid if every isolated point of the spectrum is a pole of the resolvent. The "polaroid" condition is related to the conditions of being left polaroid, right polaroid, or a-polaroid. In this paper we explore all these conditions under commuting perturbations K. As a consequence, we give a general framework from which we obtain, and also extend, recent results concerning Weyl type theorems (generalized or not) for T + K, where K is an...

Polynomial approximations and universality

A. Mouze (2010)

Studia Mathematica

We give another version of the recently developed abstract theory of universal series to exhibit a necessary and sufficient condition of polynomial approximation type for the existence of universal elements. This certainly covers the case of simultaneous approximation with a sequence of continuous linear mappings. In the case of a sequence of unbounded operators the same condition ensures existence and density of universal elements. Several known results, stronger statements or new results can be...

Currently displaying 161 – 180 of 420