We show that the set of bounded linear operators from X to X admits a Bishop–Phelps–Bollobás type theorem for numerical radius whenever X is `1(C) or c0(C). As an essential tool we provide two constructive versions of the classical Bishop–Phelps– Bollobás theorem for `1(C).

Weighted automata over the tropical semiring Zmax = (Z ∪ {−∞},max,+) are closely related to finitely generated semigroups of matrices over Zmax. In this paper, we use results in automata theory to study two quantities associated with sets of matrices: the joint spectral radius and the ultimate rank. We prove that these two quantities are not computable over the tropical semiring, i.e. there is ...

We classify the growth of a k-regular sequence based on information from its k-kernel. In order to provide such a classification, we introduce the notion of a growth exponent for k-regular sequences and show that this exponent is equal to the joint spectral radius of any set of a special class of matrices determined by the k-kernel.

Acknowledgements I first would like to thank my promotor Vincent Blondel for accepting me as his first Ph.D student, and providing me with a challenging research subject. His constructive comments, his pragmatism and his initiative were essential in the realization of this thesis. Several researchers contributed to this thesis. I would like to especially thank Alexander Vladimirov and Yurii Nes...

ABSTRAer. In Ihis note we discusa sorne results oit numerical radius altaining operators paralleling carlier results Oit norm attaining operatora. Eorarbitrary Banach spacesXand Y, the set of (bounded, linear) operatora from Xto Ywhose adjoints altain [heir norms is norm-dense ita [hespaee of ah operators. This theorem. due toW. Zizíer, improves an earlier result by J. Lindenstrauss on the dens...

Denote by w(A) the numerical radius of a bounded linear operator A acting on Hilbert space. Suppose that A is invertible and that w(A) ≤ 1+ε and w(A−1) ≤ 1+ε for some ε ≥ 0. It is shown that inf{‖A−U‖ : U unitary} ≤ cε for some constant c > 0. This generalizes a result due to J.G. Stampfli, which is obtained for ε = 0. An example is given showing that the exponent 1/4 is optimal. The more gener...

Abstract. We introduce a numerical radius operator space (X,Wn). The conditions to be a numerical radius operator space are weaker than the Ruan’s axiom for an operator space (X,On). Let w(·) be the numerical radius norm on B(H). It is shown that if X admits a norm Wn(·) on the matrix space Mn(X) which satisfies the conditions, then there is a complete isometry, in the sense of the norms Wn(·) ...

in this paper, formation of wrinkling in bimetal deep drawing process has been investigated by the analytical, numerical and experimental methods. the effects of width of flange, fillet radii of matrix and punch, clearance of blank holder, contact conditions and relative thickness of two sheets on the number and height of wrinkle waves are studied. clearance and contact conditions have the grea...

Let A be an n n complex matrix and r be the maximum size of its principal submatrices with no o¤-diagonal zero entries. Suppose A has zero main diagonal and x is a unit n-vector. Then, letting kAk be the Frobenius norm of A; we show that jhAx;xij (1 1=2r 1=2n) kAk : This inequality is tight within an additive term O n 2 : If the matrix A is Hermitian, then jhAx;xij (1 1=r) kAk : This inequality...

Background & Aims: Metaphysical distal radius fractures are common fractures account for almost half of the fractures in Orthopaedic Emergencies. According to different studies, 1-6 weeks cast immobilization after distal radius surgery has been recommended. The aim of this study was to compare outcomes and complications of short-term and long-term immobilization treatment methods. Methods: In a...