Finite dimensional projection constants

Lipschitz Extension Constants Equal Projection Constants

For a Banach space V we define its Lipschitz extension constant, LE(V ), to be the infimum of the constants c such that for every metric space (Z, ρ), every X ⊂ Z, and every f : X → V , there is an extension, g, of f to Z such that L(g) ≤ cL(f), where L denotes the Lipschitz constant. The basic theorem is that when V is finite-dimensional we have LE(V ) = PC(V ) where PC(V ) is the well-known p...

Allometry constants of finite-dimensional spaces: theory and computations

We describe the computations of some intrinsic constants associated to an n-dimensional normed space V, namely the N -th “allometry” constants κ∞(V) := inf { ‖T‖ · ‖T ′‖, T : `∞ → V, T ′ : V → `∞, TT ′ = IdV } . These are related to Banach–Mazur distances and to several types of projection constants. We also present the results of our computations for some low-dimensional spaces such as sequenc...

Numerical Estimation of Projection Constants

On Maximal Relative Projection Constants

This article focuses on the maximum of relative projection constants over all m-dimensional subspaces of the N -dimensional coordinate space equipped with the max-norm. This quantity, called maximal relative projection constant, is studied in parallel with a lower bound, dubbed quasimaximal relative projection constant. Exploiting elegant expressions for these quantities, we show how they can b...

Finite-State Temporal Projection

Finite-state methods are applied to determine the consequences of events, represented as strings of sets of fluents. Developed to flesh out events used in natural language semantics, the approach supports reasoning about action in AI, including the frame problem and inertia. Representational and inferential aspects of the approach are explored, centering on conciseness of language, context upda...