ScholarLens Back to search
2009•Bulletin of the Australian Mathematical SocietyOpen access

ISOMETRIES AND SPECTRA OF MULTIPLICATION OPERATORS ON THE BLOCH SPACE

Robert F. Allen, Flavia Colonna

Open full text 26 citations

Abstract

Abstract In this paper, we establish bounds on the norm of multiplication operators on the Bloch space of the unit disk via weighted composition operators. In doing so, we characterize the isometric multiplication operators to be precisely those induced by constant functions of modulus 1. We then describe the spectrum of the multiplication operators in terms of the range of the symbol. Lastly, we identify the isometries and spectra of a particular class of weighted composition operators on the Bloch space.

Open-access reader

About this research paper

What this paper is about

Abstract In this paper, we establish bounds on the norm of multiplication operators on the Bloch space of the unit disk via weighted composition operators. In doing so, we characterize the isometric multiplication operators to be precisely those induced by constant functions of modulus 1. We then describe the spectrum of the multiplication operators in terms of the range of the symbol. Lastly, we identify the isometries and spectra of a particular class of weighted composition operators on the Bloch space.

Why it matters

OpenAlex reports 26 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

Abstract In this paper, we establish bounds on the norm of multiplication operators on the Bloch space of the unit disk via weighted composition operators. In doing so, we characterize the isometric multiplication operators to be precisely those induced by constant functions of modulus 1. We then describe the spectrum of the multiplication operators in terms of the range of the symbol. Lastly, we identify the isometries and spectra of a particular class of weighted composition operators on the Bloch space.

Key concepts: Mathematics, Multiplication (music), Bloch space, Multiplication operator, Operator theory, Operator norm, Norm (philosophy), Spectral theorem

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
ISOMETRIES AND SPECTRA OF MULTIPLICATION OPERATORS ON THE BLOCH SPACE — Research Paper | ScholarLens