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Weighted norm estimates and L p -spectral independence of linear operators

Peer C. Kunstmann, Hendrik Vogt (2007)

Colloquium Mathematicae

We investigate the L p -spectrum of linear operators defined consistently on L p ( Ω ) for p₀ ≤ p ≤ p₁, where (Ω,μ) is an arbitrary σ-finite measure space and 1 ≤ p₀ < p₁ ≤ ∞. We prove p-independence of the L p -spectrum assuming weighted norm estimates. The assumptions are formulated in terms of a measurable semi-metric d on (Ω,μ); the balls with respect to this semi-metric are required to satisfy a subexponential volume growth condition. We show how previous results on L p -spectral independence can be treated...

Weighted projections into closed subspaces

G. Corach, G. Fongi, A. Maestripieri (2013)

Studia Mathematica

We study A-projections, i.e. operators on a Hilbert space 𝓗 which act as projections when a seminorm is considered in 𝓗. The A-projections were introduced by Mitra and Rao (1974) for finite-dimensional spaces. We relate this concept to the theory of compatibility between positive operators and closed subspaces of 𝓗. We also study the relationship between weighted least squares problems and compatibility.

Weighted pseudo almost automorphic functions with applications to abstract dynamic equations on time scales

Chao Wang, Yongkun Li (2013)

Annales Polonici Mathematici

We propose a concept of weighted pseudo almost automorphic functions on almost periodic time scales and study some important properties of weighted pseudo almost automorphic functions on almost periodic time scales. As applications, we obtain the conditions for the existence of weighted pseudo almost automorphic mild solutions to a class of semilinear dynamic equations on almost periodic time scales.

Weighted shift operators on lp spaces.

Lucas Jódar (1986)

Stochastica

The analytic-spectral structure of the commutant of a weighted shift operator defined on a lp space (1 ≤ p &lt; ∞) is studied. The cases unilateral, bilateral and quasinilpotent are treated. We apply the results to study certain questions related to unicellularity, strictly cyclicity and the existence of hyperinvariant subspaces.

Weighted sub-Bergman Hilbert spaces

Maria Nowak, Renata Rososzczuk (2014)

Annales UMCS, Mathematica

We consider Hilbert spaces which are counterparts of the de Branges-Rovnyak spaces in the context of the weighted Bergman spaces A2α, −1 < α < ∞. These spaces have already been studied in [8], [7], [5] and [1]. We extend some results from these papers

Weighted sub-Bergman Hilbert spaces in the unit disk

Ali Abkar, B. Jafarzadeh (2010)

Czechoslovak Mathematical Journal

We study sub-Bergman Hilbert spaces in the weighted Bergman space A α 2 . We generalize the results already obtained by Kehe Zhu for the standard Bergman space A 2 .

Well-posedness of second order degenerate differential equations in vector-valued function spaces

Shangquan Bu (2013)

Studia Mathematica

Using known results on operator-valued Fourier multipliers on vector-valued function spaces, we give necessary or sufficient conditions for the well-posedness of the second order degenerate equations (P₂): d/dt (Mu’)(t) = Au(t) + f(t) (0 ≤ t ≤ 2π) with periodic boundary conditions u(0) = u(2π), (Mu’)(0) = (Mu’)(2π), in Lebesgue-Bochner spaces L p ( , X ) , periodic Besov spaces B p , q s ( , X ) and periodic Triebel-Lizorkin spaces F p , q s ( , X ) , where A and M are closed operators in a Banach space X satisfying D(A) ⊂ D(M). Our results...

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