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Weighted Lp spaces and pointwise ergodic theorems.

Ryotaro Sato (1995)

Publicacions Matemàtiques

In this paper we give an operator theoretic version of a recent result of F. J. Martín-Reyes and A. de la Torre concerning the problem of finding necessary and sufficient conditions for a nonsingular point transformation to satisfy the Pointwise Ergodic Theorem in Lp. We consider a positive conservative contraction T on L1 of a σ-finite measure space (X, F, μ), a fixed function e in L1 with e > 0 on X, and two positive measurable functions V and W on X. We then characterize the pairs (V,W)...

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 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.

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...

Weyl spectra and Weyl's theorem

Young Min Han, Woo Young Lee (2001)

Studia Mathematica

"Weyl's theorem" for an operator on a Hilbert space is the statement that the complement in the spectrum of the Weyl spectrum coincides with the isolated eigenvalues of finite multiplicity. In this paper we consider how Weyl's theorem survives for polynomials of operators and under quasinilpotent or compact perturbations. First, we show that if T is reduced by each of its finite-dimensional eigenspaces then the Weyl spectrum obeys the spectral mapping theorem, and further if T is reduction-isoloid...

Weyl type theorem for operator matrices

Xiaohong Cao (2008)

Studia Mathematica

Using topological uniform descent, we give necessary and sufficient conditions for Browder's theorem and Weyl's theorem to hold for an operator A. The two theorems are liable to fail for 2 × 2 operator matrices. In this paper, we explore how they survive for 2 × 2 operator matrices on a Hilbert space.

Weyl type theorems for p-hyponormal and M-hyponormal operators

Xiaohong Cao, Maozheng Guo, Bin Meng (2004)

Studia Mathematica

"Generalized Weyl's theorem holds" for an operator when the complement in the spectrum of the B-Weyl spectrum coincides with the isolated points of the spectrum which are eigenvalues; and "generalized a-Weyl's theorem holds" for an operator when the complement in the approximate point spectrum of the semi-B-essential approximate point spectrum coincides with the isolated points of the approximate point spectrum which are eigenvalues. If T or T* is p-hyponormal or M-hyponormal then for every f ∈...

Weyl's and Browder's theorems for operators satisfying the SVEP

Mourad Oudghiri (2004)

Studia Mathematica

We study Weyl's and Browder's theorem for an operator T on a Banach space such that T or its adjoint has the single-valued extension property. We establish the spectral mapping theorem for the Weyl spectrum, and we show that Browder's theorem holds for f(T) for every f ∈ 𝓗 (σ(T)). Also, we give necessary and sufficient conditions for such T to obey Weyl's theorem. Weyl's theorem in an important class of Banach space operators is also studied.

Weyl's theorem, a-Weyl's theorem and single-valued extension property.

Pietro Aiena, Carlos Carpintero (2005)

Extracta Mathematicae

In this paper we investigate the relation of Weyl's theorem, of a-Weyl's theorem and the single valued extension property. In particular, we establish necessary and sufficient conditions for a Banch space operator T to satisfy Weyl's theorem or a-Weyl's theorem, in the case in which T, or its dual T*, has the single valued extension property. These results improve similar results obtained by Curto and Han, Djordjevic S. V., Duggal B. P., and Y. M. Han. The theory is exemplified in the case of multipliers...

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