On Poncelet's maps

A Simple Proof of Poncelet's Theorem (on the Occasion of Its Bicentennial)

Theorem 1.1 (Poncelet’s Theorem). Let K and C be nondegenerate conics in general position. Suppose there is an n-sided polygon inscribed in K and circumscribed about C such that none of its vertices belongs to C (in the case whenK and C intersect or meet). Further suppose there is an (n− 1)-sided polygonal chain with vertices on K such that all its sides are tangent to C and none of its vertice...

On strongly Jordan zero-product preserving maps

In this paper, we give a characterization of strongly Jordan zero-product preserving maps on normed algebras as a generalization of  Jordan zero-product preserving maps. In this direction, we give some illustrative examples to show that the notions of strongly zero-product preserving maps and strongly Jordan zero-product preserving maps are completely different. Also, we prove that the direct p...

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.

On the pointfree counterpart of the local definition of classical continuous maps

The familiar classical result that a continuous map from a space $X$ to a space $Y$ can be defined by giving continuous maps $varphi_U: U to Y$ on each member $U$ of an open cover ${mathfrak C}$ of $X$ such that $varphi_Umid U cap V = varphi_V mid U cap V$ for all $U,V in {mathfrak C}$ was recently shown to have an exact analogue in pointfree topology, and the same was done for the familiar cla...