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 normal cycle TK associated with a convex body K ⊂ Rn is a current which in principle contains complete information about K. It is known that if a sequence of convex bodies Ki, i ∈ N, converges to a convex body K in the Hausdorff metric, then the associated normal cycles TKi converge to TK in the dual flat seminorm. We give a quantitative improvement of this convergence result by providing a...

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...

The objective of this work is to investigate a nonlocal problem involving singular and critical nonlinearities:\begin{equation*}\left\{\begin{array}{ll} ([u]_{s,p}^p)^{\sigma-1}(-\Delta)^s_p u = \frac{\lambda}{u^{\gamma}}+u^{ p_s^{*}-1 }\quad \text{in }\Omega,\\ u>0,\;\;\;\;\quad u=0,\;\;\;\;\quad }\mathbb{R}^{N}\setminus \Omega,\end{array} \right. \end{equation*} where $\Omega$ bounded domain ...

We generalize a semi-norm for the Alexander polynomial of a connected, compact, oriented 3-manifold on its first cohomology group to a seminorm for an arbitrary Laurent polynomial f on the dual vector space to the space of exponents of f . We determine a decomposition formula for this Laurent norm; an expression for the Laurent norm for f in terms of the Laurent norms for each of the irreducibl...

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...