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A moment sequence in the q-world

Anna Kula (2007)

Banach Center Publications

The aim of the paper is to present some initial results about a possible generalization of moment sequences to a so-called q-calculus. A characterization of such a q-analogue in terms of appropriate positivity conditions is also investigated. Using the result due to Maserick and Szafraniec, we adapt a classical description of Hausdorff moment sequences in terms of positive definiteness and complete monotonicity to the q-situation. This makes a link between q-positive definiteness and q-complete...

A new characterization of Anderson’s inequality in C 1 -classes

S. Mecheri (2007)

Czechoslovak Mathematical Journal

Let ℋ be a separable infinite dimensional complex Hilbert space, and let ℒ ( ℋ ) denote the algebra of all bounded linear operators on ℋ into itself. Let A = ( A 1 , A 2 , ⋯ , A n ) , B = ( B 1 , B 2 , ⋯ , B n ) be n -tuples of operators in ℒ ( ℋ ) ; we define the elementary operators Δ A , B ℒ ( ℋ ) ↦ ℒ ( ℋ ) by Δ A , B ( X ) = ∑ i = 1 n A i X B i - X . In this paper, we characterize the class of pairs of operators A , B ∈ ℒ ( ℋ ) satisfying Putnam-Fuglede’s property, i.e, the class of pairs of operators A , B ∈ ℒ ( ℋ ) such that ∑ i = 1 n B i T A i = T implies ∑ i = 1 n A i * T B i * = T for all T ∈ 𝒞 1 ( ℋ ) (trace class operators). The main result is the equivalence between this property and the fact that...

A non elliptic spectral problem related to the analysis of superconducting micro-strip lines

Anne-Sophie Bonnet-Bendhia, Karim Ramdani (2002)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

This paper is devoted to the spectral analysis of a non elliptic operator A , deriving from the study of superconducting micro-strip lines. Once a sufficient condition for the self-adjointness of operator A has been derived, we determine its continuous spectrum. Then, we show that A is unbounded from below and that it has a sequence of negative eigenvalues tending to - ∞ . Using the Min-Max principle, a characterization of its positive eigenvalues is given. Thanks to this characterization, some conditions...

A non elliptic spectral problem related to the analysis of superconducting micro-strip lines

Anne-Sophie Bonnet-Bendhia, Karim Ramdani (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper is devoted to the spectral analysis of a non elliptic operator A , deriving from the study of superconducting micro-strip lines. Once a sufficient condition for the self-adjointness of operator A has been derived, we determine its continuous spectrum. Then, we show that A is unbounded from below and that it has a sequence of negative eigenvalues tending to -∞. Using the Min-Max principle, a characterization of its positive eigenvalues is given. Thanks to this characterization, some...

A note on compact semiderivations

Matej Brešar, Yuri Turovskii (2005)

Banach Center Publications

Let 𝓐 be a Banach algebra without nonzero finite dimensional ideals. Then every compact semiderivation on 𝓐 is a quasinilpotent operator mapping 𝓐 into its radical.

A note on composition operators on spaces of real analytic functions

Paweł Domański, Michał Goliński, Michael Langenbruch (2012)

Annales Polonici Mathematici

We characterize composition operators on spaces of real analytic functions which are open onto their images. We give an example of a semiproper map φ such that the associated composition operator is not open onto its image.

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