We present some sufficient conditions for which a Banach space X has normal structure in term of the modulus of U -convexity, modulus of W ∗-convexity and the coefficient of weak orthogonality. Some known results are improved.

In this paper, we point out that the 4-vector force exerted on a particle by another particle is always in the direction orthogonal to the 4-vector velocity of the exerted particle in 4-dimensional space-time, rather than along the line joining the couple of the particles. This inference is obviously supported from the fact that the magnitude of the 4-vector velocity is always a constant. This ...

We investigate the relationship between complex symmetry of composition operators C ϕ f = ∘ induced on classical Hardy space H 2 ( D ) by an analytic self-map open unit disk and its Koenigs eigenfunction. A generalization orthogonality known as conjugate-orthogonality will play a key role in this work. show that if is Schröder map (fixes point ∈ with 0 < | ′ 1 σ eigenfunction, then symmetric on...

In this contribution, we study multivariate polynomial interpolation and quadrature rules on non-tensor product node sets linked to Lissajous curves and Chebyshev varieties. After classifying multivariate Lissajous curves and the interpolation nodes related to these curves, we derive a discrete orthogonality structure on these node sets. Using this discrete orthogonality structure, we can deriv...

In the general theory of quantum measurement, one associates a positive-semidefinite operator on $d$-dimensional Hilbert space to each $n$ possible outcomes an arbitrary measurement. special case projective these operators are pairwise Hilbert-Schmidt orthogonal, but when $n&gt;d$, orthogonality is restricted by positivity. This restriction allows us more precisely state adage: information gain...

In this paper we investigate weak contact relations C on a lattice L, in particular, the relation between various axioms for contact, and their connection to the algebraic structure of the lattice. Furthermore, we will study a notion of orthogonality which is motivated by a weak contact relation in an inner product space. Although this is clearly a spatial application, we will show that, in cas...

In this article the notions of semi weak orthogonality and semi weak factorization structure in a category $mathcal X$ are introduced. Then the relationship between semi weak factorization structures and quasi right (left) and weak factorization structures is given. The main result is a characterization of semi weak orthogonality, factorization of morphisms, and semi weak factorization structur...

Let $\mathbb{B}(\mathcal{H})$ denote the $C^{\ast}$-algebra of all bounded linear operators on a Hilbert space $\big(\mathcal{H}, \langle\cdot, \cdot\rangle\big)$. Given positive operator $A\in\B(\h)$, and number $\lambda\in [0,1]$, seminorm ${\|\cdot\|}_{(A,\lambda)}$ is defined set $\B_{A^{1/2}}(\h)$ in $\B(\h)$ having an $A^{1/2}$-adjoint. The combination sesquilinear form ${\langle \cdot, \...