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A proof of the Grünbaum conjecture

Bruce L. Chalmers, Grzegorz Lewicki (2010)

Studia Mathematica

Let V be an n-dimensional real Banach space and let λ(V) denote its absolute projection constant. For any N ∈ N with N ≥ n define λ ₙ N = s u p λ ( V ) : d i m ( V ) = n , V ⊂ l ∞ ( N ) , λₙ = supλ(V): dim(V) = n. A well-known Grünbaum conjecture [Trans. Amer. Math. Soc. 95 (1960)] says that λ₂ = 4/3. König and Tomczak-Jaegermann [J. Funct. Anal. 119 (1994)] made an attempt to prove this conjecture. Unfortunately, their Proposition 3.1, used in the proof, is incorrect. In this paper a complete proof of the Grünbaum conjecture is presented

A q-analogue of complete monotonicity

Anna Kula (2008)

Colloquium Mathematicae

The aim of this paper is to give a q-analogue for complete monotonicity. We apply a classical characterization of Hausdorff moment sequences in terms of positive definiteness and complete monotonicity, adapted to the q-situation. The method due to Maserick and Szafraniec that does not need moments turns out to be useful. A definition of a q-moment sequence appears as a by-product.

A quantified Tauberian theorem for sequences

David Seifert (2015)

Studia Mathematica

The main result of this paper is a quantified version of Ingham's Tauberian theorem for bounded vector-valued sequences rather than functions. It gives an estimate on the rate of decay of such a sequence in terms of the behaviour of a certain boundary function, with the quality of the estimate depending on the degree of smoothness this boundary function is assumed to possess. The result is then used to give a new proof of the quantified Katznelson-Tzafriri theorem recently obtained by the author...

A quantitative asymptotic theorem for contraction semigroups with countable unitary spectrum

Charles Batty, Zdzisław Brzeźniak, David Greenfield (1996)

Studia Mathematica

Let T be a semigroup of linear contractions on a Banach space X, and let X s ( T ) = x ∈ X : l i m s → ∞ ∥ T ( s ) x ∥ = 0 . Then X s ( T ) is the annihilator of the bounded trajectories of T*. If the unitary spectrum of T is countable, then X s ( T ) is the annihilator of the unitary eigenvectors of T*, and l i m s ∥ T ( s ) x ∥ = i n f ∥ x - y ∥ : y ∈ X s ( T ) for each x in X.

A quasi-affine transform of an unbounded operator

Schôichi Ôta (1995)

Studia Mathematica

Some results on quasi-affinity for bounded operators are extended to unbounded ones and normal extensions of an unbounded operator are discussed in connection with quasi-affinity.

A quasistatic bilateral contact problem with adhesion and friction for viscoelastic materials

Arezki Touzaline (2010)

Commentationes Mathematicae Universitatis Carolinae

We consider a mathematical model which describes a contact problem between a deformable body and a foundation. The contact is bilateral and is modelled with Tresca's friction law in which adhesion is taken into account. The evolution of the bonding field is described by a first order differential equation and the material's behavior is modelled with a nonlinear viscoelastic constitutive law. We derive a variational formulation of the mechanical problem and prove the existence and uniqueness result...

A quasistatic contact problem with unilateral constraint and slip-dependent friction

Arezki Touzaline (2015)

Applicationes Mathematicae

We consider a mathematical model of a quasistatic contact between an elastic body and an obstacle. The contact is modelled with unilateral constraint and normal compliance, associated to a version of Coulomb's law of dry friction where the coefficient of friction depends on the slip displacement. We present a weak formulation of the problem and establish an existence result. The proofs employ a time-discretization method, compactness and lower semicontinuity arguments.

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