Operator maps of Jensen-type

Multiplicative bijective maps on standard operator algebras

On topological transitive maps on operator algebras

We consider the transitive linear maps on the operator algebra $B(X)$for a separable Banach space $X$. We show if a bounded linear map is norm transitive on $B(X)$,then it must be hypercyclic with strong operator topology. Also we provide a SOT-transitivelinear map without being hypercyclic in the strong operator topology.

Asymptotic behavior of alternative Jensen and Jensen type functional equations

In 1941 D.H. Hyers solved the well-known Ulam stability problem for linear mappings. In 1951 D.G. Bourgin was the second author to treat the Ulam problem for additive mappings. In 1982–2005 we established the Hyers–Ulam stability for the Ulam problem of linear and nonlinear mappings. In 1998 S.-M. Jung and in 2002–2005 the authors of this paper investigated the Hyers–Ulam stability of additive ...

Non-Archimedean stability of Cauchy-Jensen Type functional equation

In this paper we investigate the generalized Hyers-Ulamstability of the following Cauchy-Jensen type functional equation$$QBig(frac{x+y}{2}+zBig)+QBig(frac{x+z}{2}+yBig)+QBig(frac{z+y}{2}+xBig)=2[Q(x)+Q(y)+Q(z)]$$ in non-Archimedean spaces

The Additive Approximation on a Four-variate Jensen-type Operator Equation

We study the Hyers-Ulam stability theory of a four-variate Jensen-type functional equation by considering the approximate remainder φ and obtain the corresponding error formulas. We bring to light the close relation between the β-homogeneity of the norm on F *-spaces and the approximate remainder φ, where we allow p, q, r , and s to be different in their Hyers-Ulam-Rassias stability.