Multiplicative Maps on Ideals of Operators Which Are Local Automorphisms

Multiplicative bijective maps on standard operator algebras

ON FINITENESS OF PRIME IDEALS IN NORMED RINGS

In a commutative Noetherian local complex normed algebra which is complete in its M-adic metric there are only finitely many closed prime ideals.

Which Linear-fractional Composition Operators Are Essentially Normal?

We characterize the essentially normal composition operators induced on the Hardy space H2 by linear fractional maps; they are either compact, normal, or (the nontrivial case) induced by parabolic non-automorphisms. These parabolic maps induce the first known examples of nontrivially essentially normal composition operators. In addition we characterize those linearfractionally induced compositi...

Almost n-Multiplicative Maps‎ between‎ ‎Frechet Algebras

For the Fr'{e}chet algebras $(A, (p_k))$ and $(B, (q_k))$ and $n in mathbb{N}$, $ngeq 2$, a linear map $T:A rightarrow B$ is called textit{almost $n$-multiplicative}, with respect to $(p_k)$ and $(q_k)$, if there exists $varepsilongeq 0$ such that$$q_k(Ta_1a_2cdots a_n-Ta_1Ta_2cdots Ta_n)leq varepsilon p_k(a_1) p_k(a_2)cdots p_k(a_n),$$for each $kin mathbb{N}$ and $a_1, a_2, ldots, a_nin A$. Th...

Decomposability and the Cyclic Behavior of Parabolic Composition Operators

This paper establishes decomposability for composition operators induced on the Hardy spaces H (1 ≤ p < ∞) by parabolic linear fractional self-maps of the unit disc that are not automorphisms. This result, along with a recent theorem of Miller and Miller [15], shows that no such composition operator is supercyclic. The work here completes part of a previous investigation [1] where the author an...