## Tokyo Journal of Mathematics

### Compact Weighted Composition Operators on Function Algebras

Hiroyuki TAKAGI

#### Abstract

A weighted endomorphism of an algebra is an endomorphism followed by a multiplier. In [6] and [4], H. Kamowitz characterized compact weighted endomorphisms of $C(X)$ and the disc algebra. In this note we define a weighted composition operator on a function algebra as a generalization of a weighted endomorphism, and characterize compact weighted composition operators on a function algebra satisfying a certain condition [Theorem 2]. This theorem not only includes Kamowitz's results as corollaries, but also has an application to compact weighted composition operators on the Hardy class $H^\infty(D)$.

#### Article information

Source
Tokyo J. Math., Volume 11, Number 1 (1988), 119-129.

Dates
First available in Project Euclid: 1 April 2010

https://projecteuclid.org/euclid.tjm/1270134266

Digital Object Identifier
doi:10.3836/tjm/1270134266

Mathematical Reviews number (MathSciNet)
MR947951

Zentralblatt MATH identifier
0663.47021

#### Citation

TAKAGI, Hiroyuki. Compact Weighted Composition Operators on Function Algebras. Tokyo J. Math. 11 (1988), no. 1, 119--129. doi:10.3836/tjm/1270134266. https://projecteuclid.org/euclid.tjm/1270134266