## Banach Journal of Mathematical Analysis

### Composition operators from Nevanlinna type spaces to Bloch type spaces

#### Abstract

Let $X$ and $Y$ be complete metric spaces of analytic functions over the unit disk in the complex plane. A linear operator $T: X \to Y$ is a bounded operator with respect to metric balls if $T$ takes every metric ball in $X$ into a metric ball in $Y$. We also say that $T$ is metrically compact if it takes every metric ball in $X$ into a relatively compact subset in $Y$. In this paper we will consider these properties for composition operators from Nevanlinna type spaces to Bloch type spaces.

#### Article information

Source
Banach J. Math. Anal., Volume 6, Number 1 (2012), 112-123.

Dates
First available in Project Euclid: 14 May 2012

https://projecteuclid.org/euclid.bjma/1337014669

Digital Object Identifier
doi:10.15352/bjma/1337014669

Mathematical Reviews number (MathSciNet)
MR2862547

Zentralblatt MATH identifier
1269.47024

Subjects
Primary: 47B33: Composition operators
Secondary: 30H15: Nevanlinna class and Smirnov class 30H30: Bloch spaces

#### Citation

Sharma, Ajay K.; Ueki, Sei-Ichiro. Composition operators from Nevanlinna type spaces to Bloch type spaces. Banach J. Math. Anal. 6 (2012), no. 1, 112--123. doi:10.15352/bjma/1337014669. https://projecteuclid.org/euclid.bjma/1337014669