Composition operators with weak hyponormality

Abstract

There are many operator classes that are weaker than p-hyponormal. These include p-quasihyponormal, absolute p-paranormal, p-paranormal, normaloid, and spectraloid. In this note, we discuss measure theoretic composition operators in these classes.

Some Weak Hyponormal Classes of Weighted Composition Operators

“…Some results of the next section are generalizations of the work done in [3] and [4]. In those work Charles Burnap, Il Bong Jung and Alan Lambert determined when measure theoretic composition operators were p-hyponormal, w-hyponormal and other classes that are weaker than p-hyponormal.…”

“…According to Theorem 2.3 in [3], one might conjecture that a generalization to the weighted case would say: W is p-quasihyponormal if and…”

“…Note that this interesting example was used in [3] and [4] to show that composition operators can separate almost all weak hyponormal classes. Define…”

Block Matrix Operators and Weak Hyponormalities

“…(cf. [1], [4], [6], [7], [10]). Also, the study of the gap between subnormality and hyponormality has been of considerable recent interest.…”

“…Also, the study of the gap between subnormality and hyponormality has been of considerable recent interest. These studies include p-hyponormality: JungLee-Park constructed examples induced by some block matrix operators in [9] and [8], showing these classes of operators are sufficient to show the p-hyponormal classes are distinct with respect to positive real numbers p. In [1] and [2] BurnapJung-Lambert discussed some composition operator models C T on L 2 , that also…”