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Transition operators on co-compact G-spaces.

Laurent Saloff-Coste, Wolfgang Woess (2006)

Revista Matemática Iberoamericana

We develop methods for studying transition operators on metric spaces that are invariant under a co-compact group which acts properly. A basic requirement is a decomposition of such operators with respect to the group orbits. We then introduce reduced transition operators on the compact factor space whose norms and spectral radii are upper bounds for the Lp-norms and spectral radii of the original operator. If the group is amenable then the spectral radii of the original and reduced operators coincide,...

Two-dimensional real symmetric spaces with maximal projection constant

Bruce Chalmers, Grzegorz Lewicki (2000)

Annales Polonici Mathematici

Let V be a two-dimensional real symmetric space with unit ball having 8n extreme points. Let λ(V) denote the absolute projection constant of V. We show that λ ( V ) ≤ λ ( V n ) where V n is the space whose ball is a regular 8n-polygon. Also we reprove a result of [1] and [5] which states that 4 / π = λ ( l ₂ ( 2 ) ) ≥ λ ( V ) for any two-dimensional real symmetric space V.

Uniformly convex operators and martingale type.

Jörg Wenzel (2002)

Revista Matemática Iberoamericana

The concept of uniform convexity of a Banach space was gen- eralized to linear operators between Banach spaces and studied by Beauzamy [1]. Under this generalization, a Banach space X is uniformly convex if and only if its identity map Ix is. Pisier showe

Variations on Yano's extrapolation theorem.

David E. Edmunds, Miroslav Krbec (2005)

Revista Matemática Complutense

We give very short and transparent proofs of extrapolation theorems of Yano type in the framework of Lorentz spaces. The decomposition technique developed in Edmunds-Krbec (2000) enables us to obtain known and new results in a unified manner.

Young's (in)equality for compact operators

Gabriel Larotonda (2016)

Studia Mathematica

If a,b are n × n matrices, T. Ando proved that Young’s inequality is valid for their singular values: if p > 1 and 1/p + 1/q = 1, then λ k ( | a b * | ) ≤ λ k ( 1 / p | a | p + 1 / q | b | q ) for all k. Later, this result was extended to the singular values of a pair of compact operators acting on a Hilbert space by J. Erlijman, D. R. Farenick and R. Zeng. In this paper we prove that if a,b are compact operators, then equality holds in Young’s inequality if and only if | a | p = | b | q .

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