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Perturbations of the H∞-calculus

N.J. Kalton (2007)

Collectanea Mathematica

Suppose A is a sectorial operator on a Banach space X, which admits an H∞-calculus. We study conditions on a multiplicative perturbation B of A which ensure that B also has an H∞-calculus. We identify a class of bounded operators T : X→X, which we call strongly triangular, such that if B = (1 + T) A is sectorial then it also has an H∞-calculus. In the case X is a Hilbert space an operator is strongly triangular if and only if ∑ Sn(T)/n <∞ where (Sn(T))n=1∞ are the singular values of T.

Perturbed Toeplitz operators and radial determinantal processes

Torsten Ehrhardt, Brian Rider (2013)

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

We study a class of rotation invariant determinantal ensembles in the complex plane; examples include the eigenvalues of Gaussian random matrices and the roots of certain families of random polynomials. The main result is a criterion for a central limit theorem to hold for angular statistics of the points. The proof exploits an exact formula relating the generating function of such statistics to the determinant of a perturbed Toeplitz matrix.

Pexider type operators and their norms in X λ spaces

Abbas Najati, Themistocles M. Rassias (2009)

Czechoslovak Mathematical Journal

In this paper, we introduce Pexiderized generalized operators on certain special spaces introduced by Bielecki-Czerwik and investigate their norms.

Plus-operators in Krein spaces and dichotomous behavior of irreversible dynamical systems with discrete time

V. Khatskevich, L. Zelenko (2006)

Studia Mathematica

We study dichotomous behavior of solutions to a non-autonomous linear difference equation in a Hilbert space. The evolution operator of this equation is not continuously invertible and the corresponding unstable subspace is of infinite dimension in general. We formulate a condition ensuring the dichotomy in terms of a sequence of indefinite metrics in the Hilbert space. We also construct an example of a difference equation in which dichotomous behavior of solutions is not compatible with the signature...

Podal subspaces on the unit polydisk

Kunyu Guo (2002)

Studia Mathematica

Beurling's classical theorem gives a complete characterization of all invariant subspaces in the Hardy space H²(D). To generalize the theorem to higher dimensions, one is naturally led to determining the structure of each unitary equivalence (resp. similarity) class. This, in turn, requires finding podal (resp. s-podal) points in unitary (resp. similarity) orbits. In this note, we find that H-outer (resp. G-outer) functions play an important role in finding podal (resp. s-podal) points. By the methods...

Points fixes et théorèmes ergodiques dans les espaces L¹(E)

Mourad Besbes (1992)

Studia Mathematica

We prove that for each linear contraction T : X → X (∥T∥ ≤ 1), the subspace F = {x ∈ X : Tx = x} of fixed points is 1-complemented, where X is a suitable subspace of L¹(E*) and E* is a separable dual space such that the weak and weak* topologies coincide on the unit sphere. We also prove some related fixed point results.

Pointwise limit theorem for a class of unbounded operators in r -spaces

Ryszard Jajte (2007)

Studia Mathematica

We distinguish a class of unbounded operators in r , r ≥ 1, related to the self-adjoint operators in ². For these operators we prove a kind of individual ergodic theorem, replacing the classical Cesàro averages by Borel summability. The result is equivalent to a version of Gaposhkin’s criterion for the a.e. convergence of operators. In the proof, the theory of martingales and interpolation in r -spaces are applied.

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 .

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.

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...

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