In this paper, we establish several characterizations of the A-parallelism bounded linear operators with respect to seminorm induced by a positive operator A acting on complex Hilbert space. Among other things, investigate relationship between A-seminorm-parallelism and A-Birkhoff–James orthogonality A-bounded operators. particular, characterize which satisfy A-Daugavet equation. addition, rela...

The aim of this paper was to introduce and investigate a new seminorm operator tuples on complex Hilbert space H when an additional semi-inner product structure defined by positive (semi-definite) A is considered. We prove the equality between well-known A-joint in case A-doubly-commuting A-hyponormal operators. This study extension result [Results Math 75, 93(2020)] allows us show that followi...

A definition of oblique projections onto closed convex sets that use seminorms induced by diagonal matrices which may have zeros on the diagonal is introduced. Existence and uniqueness of such projections are secured via directional affinity of the sets with respect to the diagonal matrices involved. A blockiterative algorithmic scheme for solving the convex feasibility problem, employing semin...

We show that standard deviation σ satisfies the Leibniz inequality σ(fg) ≤ σ(f)‖g‖ + ‖f‖σ(g) for bounded functions f, g on a probability space, where the norm is the supremum norm. A related inequality that we refer to as “strong” is also shown to hold. We show that these in fact hold also for noncommutative probability spaces. We extend this to the case of matricial seminorms on a unital C*-al...

The convergence of the minimal energy interpolatory splines on the unit sphere is studied in this paper. An upper bound on the difference between a sufficiently smooth function and its interpolatory spherical spline in the infinity norm is given. The error bound is expressed in terms of a second order spherical Sobolev-type seminorm of the original function. §

An output least-squares type functional is employed to identify the Lamé parameters in linear elasticity. To be able to identify even the discontinuous Lamé parameters the regularization is performed by the BV-seminorm. Finite element discretization is used and convergence analysis is given. Numerical examples are given to show the feasibility of the approach. c © 2008 Elsevier Ltd. All rights ...

In this paper we study finite-difference approximations to the variational problem using the BV smoothness penalty that was introduced in an image smoothing context by Rudin, Osher, and Fatemi. We give a dual formulation for an upwind finite-difference approximation for the BV seminorm; this formulation is in the same spirit as one popularized by the first author for a simpler, less isotropic, ...

In this paper we study finite-difference approximations to the variational problem using the BV smoothness penalty that was introduced in an image smoothing context by Rudin, Osher, and Fatemi. We give a dual formulation for an “upwind” finite-difference approximation for the BV seminorm; this formulation is in the same spirit as one popularized by Chambolle for a simpler, more anisotropic, fin...

In this paper we study finite-difference approximations to the variational problem using the BV smoothness penalty that was introduced in an image smoothing context by Rudin, Osher, and Fatemi. We give a dual formulation for an upwind finite-difference approximation for the BV seminorm; this formulation is in the same spirit as one popularized by the first author for a simpler, less isotropic, ...