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Duality of measures of non-𝒜-compactness

Juan Manuel Delgado, Cándido Piñeiro (2015)

Studia Mathematica

Let be a Banach operator ideal. Based on the notion of -compactness in a Banach space due to Carl and Stephani, we deal with the notion of measure of non–compactness of an operator. We consider a map χ (respectively, n ) acting on the operators of the surjective (respectively, injective) hull of such that χ ( T ) = 0 (respectively, n ( T ) = 0 ) if and only if the operator T is -compact (respectively, injectively -compact). Under certain conditions on the ideal , we prove an equivalence inequality involving χ ( T * ) and n d ( T ) ....

Dunford-Pettis operators on the space of Bochner integrable functions

Marian Nowak (2011)

Banach Center Publications

Let (Ω,Σ,μ) be a finite measure space and let X be a real Banach space. Let L Φ ( X ) be the Orlicz-Bochner space defined by a Young function Φ. We study the relationships between Dunford-Pettis operators T from L¹(X) to a Banach space Y and the compactness properties of the operators T restricted to L Φ ( X ) . In particular, it is shown that if X is a reflexive Banach space, then a bounded linear operator T:L¹(X) → Y is Dunford-Pettis if and only if T restricted to L ∞ ( X ) is ( τ ( L ∞ ( X ) , L ¹ ( X * ) ) , | | · | | Y ) -compact.

Dyadic BMO on the bidisk.

Oscar Blanco, Sandra Pott (2005)

Revista Matemática Iberoamericana

We give several new characterizations of the dual of the dyadic Hardy space H1,d(T2), the so-called dyadic BMO space in two variables and denoted BMOdprod. These include characterizations in terms of Haar multipliers, in terms of the "symmetrised paraproduct" Λb, in terms of the rectangular BMO norms of the iterated "sweeps", and in terms of nested commutators with dyadic martingale transforms. We further explore the connection between BMOdprod and John-Nirenberg type inequalities, and study a scale...

Dynamical systems method for solving linear ill-posed problems

A. G. Ramm (2009)

Annales Polonici Mathematici

Various versions of the Dynamical Systems Method (DSM) are proposed for solving linear ill-posed problems with bounded and unbounded operators. Convergence of the proposed methods is proved. Some new results...

Dynamics of differentiation and integration operators on weighted spaces of entire functions

María J. Beltrán (2014)

Studia Mathematica

We investigate the dynamical behavior of the operators of differentiation and integration and the Hardy operator on weighted Banach spaces of entire functions defined by integral norms. In particular we analyze when they are hypercyclic, chaotic, power bounded, and (uniformly) mean ergodic. Moreover, we estimate the norms of the operators and study their spectra. Special emphasis is put on exponential weights.

(E,F)-Schur multipliers and applications

Fedor Sukochev, Anna Tomskova (2013)

Studia Mathematica

For two given symmetric sequence spaces E and F we study the (E,F)-multiplier space, that is, the space of all matrices M for which the Schur product M ∗ A maps E into F boundedly whenever A does. We obtain several results asserting continuous embedding of the (E,F)-multiplier space into the classical (p,q)-multiplier space (that is, when E = l p , F = l q ). Furthermore, we present many examples of symmetric sequence spaces E and F whose projective and injective tensor products are not isomorphic to any subspace...

Eigenvalues and subelliptic estimates for non-selfadjoint semiclassical operators with double characteristics

Michael Hitrik, Karel Pravda-Starov (2013)

Annales de l’institut Fourier

For a class of non-selfadjoint h –pseudodifferential operators with double characteristics, we give a precise description of the spectrum and establish accurate semiclassical resolvent estimates in a neighborhood of the origin. Specifically, assuming that the quadratic approximations of the principal symbol of the operator along the double characteristics enjoy a partial ellipticity property along a suitable subspace of the phase space, namely their singular space, we give a precise description of...

Eigenvalues of Hille-Tamarkin operators and geometry of Banach function spaces

Thomas Kühn, Mieczysław Mastyło (2011)

Studia Mathematica

We investigate how the asymptotic eigenvalue behaviour of Hille-Tamarkin operators in Banach function spaces depends on the geometry of the spaces involved. It turns out that the relevant properties are cotype p and p-concavity. We prove some eigenvalue estimates for Hille-Tamarkin operators in general Banach function spaces which extend the classical results in Lebesgue spaces. We specialize our results to Lorentz, Orlicz and Zygmund spaces and give applications to Fourier analysis. We are also...

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