Let T and S be two bounded linear operators from Banach spaces X into Y and suppose that T is Fredholm and the stability number k(T ;S) is 0. Let d(T ;S) be the supremum of all r > 0 such that dimN(T − λS) and codim R(T − λS) are constant for all λ with |λ| < r. It was proved in 1980 by H. Bart and D.C. Lay that d(T ;S) = limn→∞ γn(T ;S) , where γn(T ;S) are some non-negative (extended) real nu...

In 2003, Araujo and Jarosz showed that every bijective linear map θ : A → B between unital standard operator algebras preserving zero products in two ways is a scalar multiple of an inner automorphism. Later in 2007, Zhao and Hou showed that similar results hold if both A,B are unital standard algebras on Hilbert spaces and θ preserves range or domain orthogonality. In particular, such maps are...

This paper is concerned with the reduction of the spectral problem for symmetric linear operator pencils to a spectral problem for the single operator. Also, a Rayleigh–Ritz–like bounds on eigenvalues of linear operator pencils are obtained.

We discuss some linear algebra related to the Dirac matrix D of a finite simple graph G = (V,E).

In the paper [J. Math. Phys. 50 (2009), 095215, 42 pages], Feigin, Hashizume, Hoshino, Shiraishi, and Yanagida constructed two families of commuting operators which contain the Macdonald operator (commutative families of the Macdonald operator). They used the Ding–Iohara–Miki algebra and the trigonometric Feigin–Odesskii algebra. In the previous paper [arXiv:1301.4912], the present author const...

The purpose of the present article is to study and introduce family holomorphic univalent functions defined on open unit disk incluing linear operators reduced by using convolution concept between two familiar introduced many authors also studied in various families generalized starlike convex functions. Also, mathematicians considered these families, our deals with Bord distribution series, we...

We consider here a new type of mixed local and nonlocal equation under suitable Neumann conditions. discuss the spectral properties associated to weighted eigenvalue problem present global bound for subsolutions. The condition that we take into account comprises, as particular case, one has been recently introduced in (Rev. Mat. Iberoam. 33(2) (2017), 377–416). Also, results find natural applic...