We present necessary and sufficient conditions for the reducibility of a self-adjoint linear relation in Krein space. Then generalized Nevanlinna function Q represented by A Pontryagin space can be decomposed means reducing subspaces A. The sum two functions $$ {Q}_i\in {N}_{\kappa_i}\left(\mathcal{H}\right) , i = 1, 2, minimally triplets \left({\mathcal{K}}_i,{A}_i,{\Gamma}_i\right) is also st...

Let C(d, n) denote the set of d-dimensional lattice paths using the steps X1 := (1, 0, . . . , 0), X2 := (0, 1, . . . , 0), . . . , Xd := (0, 0, . . . , 1), running from (0, 0, . . . , 0) to (n, n, . . . , n), and lying in {(x1, x2, . . . , xd) : 0 ≤ x1 ≤ x2 ≤ . . . ≤ xd}. On any path P := p1p2 . . . pdn ∈ C(d, n), define the statistics asc(P ) :=|{i : pipi+1 = XjX`, j < `}| and des(P ) :=|{i :...

In this paper, we study the generalized Jordan-von Neumann constant and obtain its estimates for the normal structure coefficient N(X), improving the known results of S. Dhompongsa.

In the recent literature, constraints on the CKM angle arising from the branching ratios for B ! K and B d ! K decays received a lot of attention. An important theoretical limitation of the accuracy of these bounds is due to rescat-tering eeects, such as B + ! f 0 K + g ! + K 0. We point out that these processes are related to penguin topologies with internal up quark exchanges and derive SU (2...

Let $R$ be a ring and $Z(R)$ the center of $R.$ The aim this paper is to define notions centrally extended Jordan derivations $\ast$-derivations, prove some results involving these mappings. Precisely, we that if $2$-torsion free noncommutative prime admits derivation (resp. $\ast$-derivation) $\delta:R\to R$ such that\[[\delta(x),x]\in Z(R)~~(resp.~~[\delta(x),x^{\ast}]\in Z(R))\text{ for all ...

In this paper identities related to derivations on semiprime rings and standard operator algebras are investigated. We prove the following result which generalizes a classical result of Chernoff. Let X be a real or complex Banach space, let L(X) be the algebra of all bounded linear operators of X into itself and let A(X) ⊆ L(X) be a standard operator algebra. Suppose there exists a linear mappi...

let  be a banach algebra. let  be linear mappings on . first we demonstrate a theorem concerning the continuity of double derivations; especially that all of -double derivations are continuous on semi-simple banach algebras, in certain case. afterwards we define a new vocabulary called “-higher double derivation” and present a relation between this subject and derivations and finally give some ...