Let V = B(H) or S(H), where B(H) is the algebra of bounded linear operator acting on the Hilbert space H, and S(H) is the set of self-adjoint operators in B(H). Denote the numerical range of A ∈ B(H) by W (A) = {(Ax, x) : x ∈ H, (x, x) = 1}. It is shown that a surjective map φ : V→ V satisfies W (AB +BA) =W (φ(A)φ(B) + φ(B)φ(A)) for all A,B ∈ V if and only if there is a unitary operator U ∈ B(H...

In this work, we define the joint normal eigenvalue, joint reducing approximate eigenvalue and we obtain some important and new results about the boundary of joint numerical range of n-tuple operators on a complex Hilbert space.

The main purpose of this article is to show that the numerical range a linear pencil λA+B equal C if and only 0 belongs convex hull joint A B. We also prove A+A⁎,B+B⁎⩾0, then B have common isotropic vector. Moreover, we improve classical result which describes Hermitian pencils.

We prove new enclosures for the spectrum of non-selfadjoint operator matrices associated with second order linear differential equations z̈(t) +Dż(t) +A0z(t) = 0 in a Hilbert space. Our main tool is the quadratic numerical range for which we establish the spectral inclusion property under weak assumptions on the operators involved; in particular, the damping operator only needs to be accretive a...

 ‎Let $V$ be an $n$-dimensional complex inner product space‎. ‎Suppose‎ ‎$H$ is a subgroup of the symmetric group of degree $m$‎, ‎and‎ ‎$chi‎ :‎Hrightarrow mathbb{C} $ is an irreducible character (not‎ ‎necessarily linear)‎. ‎Denote by $V_{chi}(H)$ the symmetry class‎ ‎of tensors associated with $H$ and $chi$‎. ‎Let $K(T)in‎ (V_{chi}(H))$ be the operator induced by $Tin‎ ‎text{End}(V)$‎. ‎Th...

We introduce and investigate the orbit-closed $C$-numerical range, a natural modification of range an operator introduced for $C$ trace-class by Dirr vom Ende. Our is conservative theirs because these two sets have same closure even coincide when finite rank. Since Ende's results concerning depend only on its closure, our inherits properties, but we also establish more. For selfadjoint, Ende we...

For any n×n matrix A , we use the joint higher rank numerical range, Λk(A, . . . ,Am) , to define the higher rank numerical hull of A . We characterize the higher rank numerical hulls of Hermitian matrices. Also, the higher rank numerical hulls of unitary matrices are studied. Mathematics subject classification (2010): 15A60,81P68.

This work studies the Voce–Chaboche (V–C) material model parameter optimization for high-strength steel welded joints subjected to cyclic loading. The parameters of each zone in a S690 butt-welded joint were determined using an algorithm based on Newton trust region (NTR) method and accumulated true strain parameter. fitted stress–strain histories from uniaxial strain-controlled tests. To valid...

Abstract. Let T1, . . . , Tn be bounded linear operators on a complex Hilbert space H. Then there are compact operators K1, . . . , Kn ∈ B(H) such that the closure of the joint numerical range of the n-tuple (T1−K1, . . . , Tn−Kn) equals to the joint essential numerical range of (T1, . . . , Tn). This generalizes the corresponding result for n = 1. We also show that if S ∈ B(H) and n ∈ N then t...