Bounds for the operator norms

of some Nörlund matrices

Authors:
P. D. Johnson Jr., R. N. Mohapatra Jr. and David Ross Jr.

Journal:
Proc. Amer. Math. Soc. **124** (1996), 543-547

MSC (1991):
Primary 40G05

DOI:
https://doi.org/10.1090/S0002-9939-96-03081-X

MathSciNet review:
1301506

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Abstract | References | Similar Articles | Additional Information

Abstract: Suppose is a non-increasing sequence of non-negative numbers with , , , and is the lower triangular matrix defined by , , and , . We show that the operator norm of as a linear operator on is no greater than , for ; this generalizes, yet again, Hardy's inequality for sequences, and simplifies and improves, in this special case, more generally applicable results of D. Borwein, Cass, and Kratz. When the tend to a positive limit, the operator norm of on is exactly . We also give some cases when the operator norm of on is less than .

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Additional Information

**P. D. Johnson Jr.**

Affiliation:
Department of Discrete and Statistical Sciences 120 Math Annex Auburn University, Alabama 36849-5307

Email:
johnspd@mail.auburn.edu

**R. N. Mohapatra Jr.**

Affiliation:
Department of Mathematics University of Central Florida Orlando, Florida 32816-6690

**David Ross Jr.**

Affiliation:
Department of Mathematics Embry Riddle Aeronautical University Daytona Beach, Florida 32114

DOI:
https://doi.org/10.1090/S0002-9939-96-03081-X

Received by editor(s):
February 4, 1994

Received by editor(s) in revised form:
September 7, 1994

Communicated by:
J. Marshall Ash

Article copyright:
© Copyright 1996
American Mathematical Society