Vol. 30, No. 2, 1969

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Vol. 320: 1  2
Vol. 319: 1  2
Vol. 318: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Contacts
 
Submission Guidelines
Submission Form
Policies for Authors
 
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
 
Other MSP Journals
A subcollection of algebras in a collection of Banach spaces

Robert Paul Kopp

Vol. 30 (1969), No. 2, 433–435
Abstract

Let D(p,r) with 1 p < and −∞ < r < +denote the Banach space consisting of certain analytic functions f(z) defined in the unit disk. A function f(z) = n=0anzn is a member of D(p,r) if and only if

∑∞       r   p
(n +1) |an |< ∞.
n=0

We define the norm of f in D(p,r) by

        ∑∞       r   p
∥f∥p.r = (  (n+ 1) |an| )1∕p.
n=0

By the product of two functions f and g in D(p,r) we shall mean their product as functions, i.e., [f.g](z) = f(z)g(z). The purpose of this paper is to discover which of the spaces D(p,r) are algebras.

Mathematical Subject Classification
Primary: 46.55
Milestones
Received: 26 February 1968
Published: 1 August 1969
Authors
Robert Paul Kopp